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Life and Activities of David Gordeziani

  • George JaianiEmail author
  • Temur Jangveladze
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 276)

Abstract

David Gordeziani was born in Tbilisi on December 9 of 1937. Since 1945 attended Tbilisi Secondary School No 1, which he graduated with the gold medal in 1956. In the same year he became a student of the faculty of Mechanics and Mathematics at Ivane Javakhishvili Tbilisi State University (TSU).

References

  1. 1.
    Abuladze, I.O., Gordeziani, D.G., Dzhangveladze, T.A., Korshiya, T.K.: Discrete Models for a nonlinear magnetic-field-scattering problem with thermal Conductivity (Russian). Differential’nye Uravnenyia, 22, 7, 1119–1129 (1986). English translation: Differential Equations, 22, 7, 769–777 (1986)Google Scholar
  2. 2.
    Abuladze, I.O., Gordeziani, D.G., Dzhangveladze, T.A., Korshiya, T.K.: On the numerical modeling of a nonlinear problem of the diffusion of a magnetic field with regard to heat conductivity. Proc. I. Vekua Inst. Appl. Math. (Tbiliss. Gos. Univ. Inst. Prikl. Math. Trudy), 18, 48–67 (1986) (Russian, Georgian and English summaries)Google Scholar
  3. 3.
    Avalishvili G., Avalishvili M., Gordeziani D.: On a hierarchical model reduction algorithm for elastic multi-structures. In: 11th World Congress on Computational Mechanics (WCCM XI), 5th European Conference on Computational Mechanics (ECCMV), 6th European Conference on Computational Fluid Dynamics (ECFDVI), July 20–25, Barcelona, Spain (2014)Google Scholar
  4. 4.
    Avalishvili G., Avalishvili M., Gordeziani D.: On construction and investigation of dynamical models for elastic multi-structures. In: The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 7–11, Madrid, Spain (2014)Google Scholar
  5. 5.
    Avalishvili, G., Avalishvili, M., Gordeziani, D.: On integral nonlocal boundary value problems for some partial differential equations. Bull. Georgian Natl. Acad. Sci. (N.S.) 5(1), 31–37 (2011)Google Scholar
  6. 6.
    Avalishvili, G., Avalishvili, M., Gordeziani, D.: On some nonclassical two-dimensio-nal models for thermoelastic plates with variable thickness. Bull. Georgian Natl. Acad. Sci. (N.S.) 4(2), 27–34 (2010)Google Scholar
  7. 7.
    Avalishvili, G., Avalishvili, M., Gordeziani, D.: Initial boundary value problem for one generalization of Schrödinger equation. Rep. Enlarged Sess. Semin. I. Vekua. Appl. Math. 20(1–3), 5–7 (2005)zbMATHGoogle Scholar
  8. 8.
    Avalishvili, G., Avalishvili, M., Gordeziani, D.: Construction and investigation of hierarchical models for thermoelastic prismatic shells. Bull. Georgian Acad. Sci. (N.S.) 2(3), 35–42 (2008)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Avalishvili, G., Avalishvili, M., Gordeziani, D.: On dynamical three-dimensional fluid-solid interaction problem. Georgian Math. J. 15(4), 601–618 (2008)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Avalishvili, G., Avalishvili, M., Gordeziani, D.: On a nonlocal problem with integral boundary conditions for a multidimensional elliptic equation. Appl. Math. Lett. 24(4), 566–571 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Avalishvili, G., Avalishvili, M., Gordeziani, D.: Investigation of statistic two-dimensional models for thermoelastic prismatic shells with microtemperatures. Bull. Georgian Natl. Acad. Sci. (N.S.) 7(3), 20–30 (2013)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Avalishvili, G., Avalishvili, M., Gordeziani, D.: On the investigation of dynamical hierarchical models of elastic multi-structures consisting of three-dimensional body and multilayer substructure. Bull. Georgian Natl. Acad. Sci. (N.S.) 8(3), 20–31 (2014)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Avalishvili, G., Avalishvili, M., Gordeziani, D., Miara, B.: Hierarchical modeling of thermoelastic plates with variable thickness. Anal. Appl. (Singap.) 8(2), 125–159 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Avalishvili, G., Gordeziani, D.: On the investigation of plurievolution equations in abstract spaces. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 14(3), 12–15 (1999)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Avalishvili, G., Gordeziani, D.: On one class of spatial nonlocal problems for some hyperbolic equations. Georgian Math. J. 7(3), 417–425 (2000)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Avalishvili, M., Gordeziani, D.: Investigation of two-dimensional models of elastic prismatic shells. Georgian Math. J. 10(1), 17–36 (2003)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Berikelashvili, G., Gordeziani, D., Kharibegashvili, S.: Finite difference scheme for one mixed problem with integral condition. In: Proceedings of the 2\(^{nd}\) WSEAS International Conference Finite Differences, Finite Elements, Finite Volumes, Boundary Elements (Eand-B 2009), Tbilisi, Georgia, June 26–28, pp. 118–120 (2009)Google Scholar
  18. 18.
    Berikelashvili, G.K., Gordeziani, D.G.: On a nonlocal generalization of the biharmonic Dirichlet problem (Russian). Differ. Uravn. 46, 3, 318-325 (2010); Translation in Differ. Equ. 46, 3, 321–328 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Berikelashvili, G., Gordeziani, D.: On a nonlocal generalization of the biharmonic Dirichlet problem. Diff. Equ. 46(3), 1–8 (2010)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Davitashvili, T., Gordeziani, D., Samkharadze, I.: Numerical modeling of oil infiltration into the soil for risk assessment. In: Book “Informational and Communication Technologies—Theory and Practice: Proceedings of the International Scientific Conference ICTMC-2010 Devoted to the 80\(^{th}\) Anniversary of I.V. Prangishvili”, Nova, USA, pp. 154-161 (2011)Google Scholar
  21. 21.
    Davitashvili, T., Gordeziani, D., Geladze, G., Sharikadze, M.: Investigation of the circumstance of the light-signals at the streets’ crossing point influence upon the harmful substances’ concentrations distribution by numerical modeling. Appl. Math. Inform. Mech. 13(2), 57–61 (2008)zbMATHGoogle Scholar
  22. 22.
    Davitashvili, T., Gordeziani, D., Khvedelidze, Z.: On the mathematical model of the Georgian transport coridor contamination. Bull. Georgian Acad. Sci. 162, 46–50 (2000)zbMATHGoogle Scholar
  23. 23.
    Ebel, A., Davitashvili, T., Elbern, H., Gordeziani, D., Jakobs, H.J., Memmesheimer, M.: Tavkhelidze I., Numerical modelling of air pollution on regional and local scales. Appl. Math. Inform. Mech. 9(2), 1–13 (2004)Google Scholar
  24. 24.
    Gordeziani, D., Avalishvili, M.: Investigation of hierarchic models of prismatic shells. Bull. Georgian Acad. Sci. 165(3,2), 485–488 (2002)Google Scholar
  25. 25.
    Gordeziani, D., Avalishvili, G.: On approximation of a dynamical problem for elastic mixtures by two-dimensional problems. Bull. Georgian Acad. Sci. 170(1), 46–49 (2004)Google Scholar
  26. 26.
    Gordeziani, D., Davitashvili, T., Davitashvili, T.: On one mathematical model of the Black Sea pollution by oil. In: Book “Informational and Communication Technologies—Theory and Practice: Proceedings of the International Scientific Conference ICTMC-2010 Devoted to the 80\(^{th}\) Anniversary of I.V. Prangishvili”, Nova, USA, pp. 140–147 (2011)Google Scholar
  27. 27.
    Gordeziani, D.G., Dzhangveladze, T.A., Korshiya, T.K.: Existence and Uniqueness of a Solution of Certain Nonlinear Parabolic Problems (Russian). Differential’nye Uravnenyia, 19, 7, 1197–1207 (1983). English translation: Differential Equations, 19, 7, 887–895 (1984)Google Scholar
  28. 28.
    Gordeziani, D., Džioev, T.: The generalization of Bitsadze-Samarski problem with reference to the problems of Baroclinic Sea’s dynamics (Russian). Outlines on physics and chemistry of the waters of the Black Sea. Moscow (1978)Google Scholar
  29. 29.
    Gordeziani, D.G., Džioev, T.Z.: The solvability of a certain boundary value problem for a nonlinear equation of elliptic type (Russian). Sakharth. SSR, Mecn. Akad. Moambe 68 289–292(1972)Google Scholar
  30. 30.
    Gordeziani, D.G., Evseev, E.G.: The Numerical Solution of a Model of an Arch Dam (Russian with Georgian and English summaries). Izdat. Tbilis. Univ, Tbilisi (1977)Google Scholar
  31. 31.
    Gordeziani, D., Gordeziani, N., Avalishvili, G.: On the investigation and resolution of nonlocal boundary and initial boundary value problems. Rep. Enlarged Sess. Semin. I. Vekua. Appl. Math. 12(3), 18–20 (1997)Google Scholar
  32. 32.
    Gordeziani, D., Gordeziani, N., Avalishvili, G.: On the investigation and resolution of nonlocal boundary and initial-boundary value problems, Rep. Enlarged Sess. Semin. I. Vekua. Appl. Math. 12(3), 60–63 (1997)Google Scholar
  33. 33.
    Gordeziani, D.G., Gordeziani, E.D., Kachiashvili, K.J.: About some mathematical models of the transport of pollutants in the rivers. In: Ninth Inter-State Conference “Problems of Ecology and Operation of Objects of the Power”, pp. 77–79. Kiev, Ukraine (1999)Google Scholar
  34. 34.
    Gordeziani, D., Gordeziani, E.: Mathematical modeling and numerical solution of some problems of water and atmosphere pollution. Manuscript for NATO ARW, "Air, Water and Soil Quality Modeling for Risk. and Impact Assessment", 16–20 September, Tabakhmela, Georgia, pp. 195–210. Springer (2005)Google Scholar
  35. 35.
    Gordeziani, D., Jangveladze, T., Korshiya, T.: A class of nonlinear diffusion equation. ICM, Warshaw (1982), Sec. 11: part. diff. eq. IX, 17 (1983)Google Scholar
  36. 36.
    Gordeziani, D.G., Komurdzhishvili, O.: Numerical solution of some boundary value problems for a variant of the theory of thin shells (Russian. with Georgian and English summaries). Izdat. Tbilis. Univ., Tbilisi (1977)Google Scholar
  37. 37.
    Gordeziani, D.G., Samarskiĭ, A.A.: Some problems of the thermoelasticity of plates and shells, and the method of summary approximation (Russian). in Coll. Complex analysis and its applications “Nauka”, Moscow 173–186 (1978)Google Scholar
  38. 38.
    Gordeziani, D.G.: A class of nonlocal boundary value problems in elasticity. theory and shell theory. In Coll. Theory and numerical methods of calculating plates and shells (Russian). Tbilis. Gos. Univ., Tbilisi, II, 106–127 (1984)Google Scholar
  39. 39.
    Gordeziani, D.G.: A numerical solution to certain problems of thermoelasticity (Russian). Izdat. Tbilis. Univ, Tbilisi (1979)Google Scholar
  40. 40.
    Gordeziani, D.G.: An additive model for parabolic equations with mixed derivatives (Russian) Current problems in mathematical physics and numerical mathematics. Nauka Moscow, 128–137 (1982)Google Scholar
  41. 41.
    Gordeziani, D.G.: Methods for Solving a Class of Nonlocal Boundary Value Problems (Russian with Georgian and English summaries). Tbilis. Gos. Univ., Inst. Prikl. Mat., Tbilisi (1981)Google Scholar
  42. 42.
    Gordeziani, D.: On application of the Total Approximation Method to the Solution Of Some Shell Theory Problems. in Coll. Theory of Shells. Nirt-Holland Publ. Company, pp. 323–325 (1980)Google Scholar
  43. 43.
    Gordeziani, D.: On solution of in time nonlocal problems for some equations of mathematical physics. ICM-94, Abstracts. Short Communications (1994)Google Scholar
  44. 44.
    Gordeziani, D.: Sur une methode aux difference finies pour la resolution d’equantions aux derives partielles. Compt. Rand. Seminars d’Analyse Numerique Univ. Paris VI, 1–8 (1971–72)Google Scholar
  45. 45.
    Gordeziani, D.: Sur une methode economique de decompositions des operateures pour la solution numerique de problemes a dimensions multiples. Compt. Rand. Seminars d’Analyse Numerique Univ. Paris VI, 87–97 (1971–72)Google Scholar
  46. 46.
    Gordeziani, D.G.: Application of a locally one-dimensional method to the solution of multi-dimensional parabolic equations of the order 2m (Russian). Soobšč. Akad. Nauk Gruzin. SSR 39, 535–541 (1965)MathSciNetGoogle Scholar
  47. 47.
    Gordeziani, D.G.: On the numerical solution of a quasilinear equation of parabolic type (Russian). Soobšč. Akad Nauk Gruzin. SSR 37, 3–10 (1965)MathSciNetGoogle Scholar
  48. 48.
    Gordeziani, D.G.: On the use of rhombic grids for the solution of the equation of heat conduction (Russian) Soobšč. Akad. Nauk Gruzin. SSR 38, 15–22 (1965)MathSciNetGoogle Scholar
  49. 49.
    Gordeziani, D.G.: A certain class of factored difference schemes (Russian). Gamoqeneb. Math. Inst. Sem. Mohsen. Anotacie 1, 25–28 (1969)MathSciNetGoogle Scholar
  50. 50.
    Gordeziani, D.G.: A certain method of solving the Bitsadze-Samarskiĭ boundary value problem (Russian). Gamoqeneb. Math. Inst. Sem. Mohsen. Anotacie 2, 39–41 (1970)MathSciNetGoogle Scholar
  51. 51.
    Gordeziani, D.G.: The regularization of nonlinear difference schemes (Russian). Gamoqueneb. Math. Inst. Sem. Mohsen. Anotacie 2, 35–37 (1970)MathSciNetGoogle Scholar
  52. 52.
    Gordeziani, D.G.: A certain economical difference method for the solution of a multidimensional equation of hyperbolic type (Russian). Gamoqeneb. Math. Inst. Sem. Mohsen. Anotacie 4, 11–14 (1971)Google Scholar
  53. 53.
    Gordeziani, D.G.: A certain way of using the additivity principle for the solution of second order evolution equations (Russian) Gamoqeneb. Math. Inst. Sem. Mohsen. Anotacie 4, 23–26 (1971)Google Scholar
  54. 54.
    Gordeziani, D.G.: On the solvability of some boundary value problems for a variant of the theory of thin shells (Russian). Dokl. Akad. Nauk SSSR 215(6), 1289–1292 (1974)MathSciNetGoogle Scholar
  55. 55.
    Gordeziani, D.G.: To the exactness of one variant of the theory of thin shells (Russian). Dokl. Akad. Nauk SSSR 216(4), 751–754 (1974)MathSciNetGoogle Scholar
  56. 56.
    Gordeziani, D.G.: A class of nonlocal boundary value problems (Russian). Current problems in mathematical physics, Tbilis. Gos. Univ. I, 183–190 (1987)Google Scholar
  57. 57.
    Gordeziani, D.G.: Finite-difference schemes for solving nonlocal boundary value problems (Russian). Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 19, 20–25 (1987)MathSciNetGoogle Scholar
  58. 58.
    Gordeziani, D.G.: On nonlocal in time problems for Navier-Stokes equations. Rep. Enlarged Sess. Semin. I. Vekua. Appl. Math. 8(3), 13–17 (1993)Google Scholar
  59. 59.
    Gordeziani, D.: Gordeziani N.: On the investigation of one problem in the linear theory of the elastic mixtures. Dokl. Semin. Inst. Prikl. Mat. im. I.N. Vekua 22, 115–122 (1993)Google Scholar
  60. 60.
    Gordeziani, D.: On rigid motions in Vekua theory of prismatic shells. Semin. I. Vekua Inst. Appl. Math. Rep. 24, 3–9 (1998)MathSciNetzbMATHGoogle Scholar
  61. 61.
    Gordeziani, D.: On rigid motions in Vekua theory of prismatic shells. Bull. Georgian Acad. Sci. 161(3), 413–416 (2000)MathSciNetzbMATHGoogle Scholar
  62. 62.
    Gordeziani, D.: Davitashvili Tinatin, Davitashvili Teimuraz, Sharikadze M.: Mathematical modeling of filtration problem for the multilayer liquid-permeable horizons. Rep. Enlarged Sess. Semin. I. Vekua Inst. Appl. Math. 30, 19–22 (2016)Google Scholar
  63. 63.
    Gordeziani, D., Avalishili, M., Avalishili, G.: Dynamical two-dimensional models of solid-fluid interaction. Differential equations and their applications. J. Math. Sci. (N.Y.) 157(1), 16–42 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  64. 64.
    Gordeziani, D., Avalishvili, G.: Investigation of the nonlocal boundary value problems for the string oscillation and telegraph equations. Appl. Math. and Informatics (AMI) 2, 65–79 (1997)MathSciNetzbMATHGoogle Scholar
  65. 65.
    Gordeziani, D., Avalishvili, G.: Nonlocal problems for a vibrating string. Bull. of Tbilisi Int. Centre Math. Inf. (TICMI) 2, 22–24 (1998)Google Scholar
  66. 66.
    Gordeziani, D., Avalishvili, G.: Nonclassical problems for the second order hyperbolic equations. Bull. TICMI 3(3), 53–57 (1999)zbMATHGoogle Scholar
  67. 67.
    Gordeziani, D., Avalishvili, G.: On the investigation of nonlocal problems in time for hyperbolic equations. Bull. Georgian Acad. Sci. 162(2), 229–232 (2000)MathSciNetzbMATHGoogle Scholar
  68. 68.
    Gordeziani, D.G., Avalishvili, G.A.: Solution of nonlocal problems for one-dimensional oscillations of a medium (Russian). Mat. Model. 12(1), 94–103 (2000)MathSciNetzbMATHGoogle Scholar
  69. 69.
    Gordeziani, D., Avalishvili, G.: Investigation of the nonlocal initial boundary value problems for some hyperbolic equations. Hirosh. Math. J. 31(3), 345–366 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  70. 70.
    Gordeziani, D., Avalishvili, G.: On the investigation of the boundary value problem for nonlinear model in the theory of elastic mixtures. Bull. Georgian Acad. Sci. 164(3), 451–453 (2001)MathSciNetzbMATHGoogle Scholar
  71. 71.
    Gordeziani, D., Avalishvili, M.: Investigation of a dynamical two-dimensional model of prismatic shells. Bull. Georgian Acad. Sci. 166(1), 16–19 (2002)MathSciNetzbMATHGoogle Scholar
  72. 72.
    Gordeziani, D., Avalishvili, G.: Investigation of nonlinear models in the theory of elastic mixtures. Appl. Math. Inform. 7(2), 41–65 (2002)MathSciNetzbMATHGoogle Scholar
  73. 73.
    Gordeziani, D., Avalishvili, G.: On a static two-dimensional model of multilayer elastic prismatic shells. Bull. Georgian Acad. Sci. 168(3), 455–457 (2003)MathSciNetGoogle Scholar
  74. 74.
    Gordeziani, D., Avalishvili, G.: On the investigation of dynamical hierarchical model of multilayer elastic prismatic shells. Bull. Georgian Acad. Sci. 168(1), 11–13 (2003)MathSciNetGoogle Scholar
  75. 75.
    Gordeziani, D., Avalishvili, G.: On static two-dimensional model of multilayer elastic prismatic shell. Bull. Georgian Acad. Sci. 168(3), 455–457 (2003)MathSciNetzbMATHGoogle Scholar
  76. 76.
    Gordeziani, D., Avalishvili, G.: On the investigation of static hierarchic models for elastic rods. Appl. Math. Inform. Mech. 8(1), 34–46 (2003)MathSciNetzbMATHGoogle Scholar
  77. 77.
    Gordeziani, D., Avalishvili, G.: On a dynamical hierarchical model for prismatic shells in the theory of elastic mixtures. Math. Meth. Appl. Sci. 28, 737–756 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  78. 78.
    Gordeziani, D.G., Avalishvili, G.A.: Time-nonlocal problems for Schrödinger type equations: I. Prol. Abstr. Spaces Diff. Equ. 41(5), 703–711 (2005)zbMATHCrossRefGoogle Scholar
  79. 79.
    Gordeziani, D.G., Avalishvili, G.A.: Time-nonlocal problems for Schrödinger type equations: II. Results Specif. Prbl. Diff. Equ. 41(6), 852–859 (2005)zbMATHCrossRefGoogle Scholar
  80. 80.
    Gordeziani, D., Avalishvili, M., Avalishvili, G.: On the Investigation of one nonclassical problem for Navier-Stokes equations. AMI 7(2), 66–77 (2002)MathSciNetzbMATHGoogle Scholar
  81. 81.
    Gordeziani, D., Avalishvili, M., Avalishvili, G.: On one method of construction of mathematical models of multistructures. Bull. Georgian Acad. Sci. 166(3), 466–469 (2002)MathSciNetzbMATHGoogle Scholar
  82. 82.
    Gordeziani, D., Avalishvili, M., Avalishvili, G.: On the investigation of one nonclassical problem for Navier-Stokes equations. Appl. Math. Inform. 7(2), 66–77 (2002)MathSciNetzbMATHGoogle Scholar
  83. 83.
    Gordeziani, D., Avalishvili, D., Avalishvili, M.: On the investigation of a dimensional reduction method for elliptic problems. Rep. Enlarged Sess. Semin. I. Vekua. Appl. Math. 29, 15–25 (2003)zbMATHGoogle Scholar
  84. 84.
    Gordeziani, D., Avalishvili, G., Avalishvili, M.: Dynamical hierarchical models for elastic shells. AMIM 10(1), 19–38 (2005)MathSciNetzbMATHGoogle Scholar
  85. 85.
    Gordeziani, D., Avalishvili, G., Avalishvili, M.: On nonclassical multi-time evolution equation in abstract spaces. Bull. Georgian Acad. Sci. 172(3), 384–387 (2005)MathSciNetzbMATHGoogle Scholar
  86. 86.
    Gordeziani, D., Avalishvili, G., Avalishvili, M.: Hierarchical models of elastic shells in curvilinear coordinates. Int. J. Comput. Math. Appl. 51, 1789–1808 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  87. 87.
    Gordeziani, D., Avalishvili, G., Avalishvili, M.: On the investigation of the generalized Schrödinger type equation in abstract spaces. Bull. Georgian Natl. Acad. Sci. 173(2), 258–261 (2006)MathSciNetzbMATHGoogle Scholar
  88. 88.
    Gordeziani, D., Avalishvili, M., Avalishvili, G.: On one-dimensional hierarchical models for elliptic problems. Georgian Int. J. Sci. Technol. Med. 1(2), 83–94 (2008)zbMATHGoogle Scholar
  89. 89.
    Gordeziani, D., Avalishvili, M., Avalishvili, G.: Dynamical two-dimensional models of solid-fluid interaction. J. Math. Sci. 157(1), 16–42 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  90. 90.
    Gordeziani, D., Davitashvili, T.: Mathematical model with nonlocal boundary condition for the atmosphere pollution. Appl. Math. Inf. 4, 30–53 (1999)zbMATHGoogle Scholar
  91. 91.
    Gordeziani, D., Davitashvili, T.: Mathematical model of the atmosphere pollution with non-classic boundary conditions. Appl. Math. Inform. 4(1), 75–92 (1999)MathSciNetzbMATHGoogle Scholar
  92. 92.
    Gordeziani, D.G., Dzhangveladze, T.A., Korshiya, T.K.: A class of nonlinear parabolic equations, that arise in problems of the diffusion of an electromagnetic field (Russian, Georgian and English summaries). Proc. I.Vekua Inst. Appl. Math. (Tbiliss. Gos. Univ. Inst. Prikl. Math. Trudy) 13, 7–35 (1983)Google Scholar
  93. 93.
    Gordeziani, D.G., Evseev, E.G.: A difference method of solving higher order multidimensional differential equations (Russian). Sakharth SSR, Mecn. Akad. Moambe 54, 281–284 (1969)MathSciNetGoogle Scholar
  94. 94.
    Gordeziani, D.G., Evseev, E.G.: The factorization of difference schemes (Russian). Sakharth SSR, Mecn. Akad. Moambe 53, 273–276 (1969)MathSciNetGoogle Scholar
  95. 95.
    Gordeziani, D.G., Evseev, E.G.: A certain difference approximation of a fourth order equation (Russian) Studies of certain equations of mathematical physics (Russian). Izdat. Tbilis 1, 37–40 (1972)Google Scholar
  96. 96.
    Gordeziani, D.G., Evseev, E.G.: The approximate solution of the equations of a certain variant of the theory of cylindrical shells with mixed boundary conditions (Russian). Sakharth. SSR, Mecn. Akad. Moambe 78(2), 297–300 (1975)MathSciNetGoogle Scholar
  97. 97.
    Gordeziani, D.G., Evseev, E.G.: An economical difference method for the solution of systems of hyperbolic equations (Russian). Sakharth SSR, Mecn. Akad. Moambe 86(3), 557–560 (1977)MathSciNetzbMATHGoogle Scholar
  98. 98.
    Gordeziani, D.G., Evseev, E.G.: Additive averaged schemes for the numerical solution of hyperbolic equations (Russian). Soobshch. Akad. Nauk Gruzin. SSR 104(2), 277–280 (1981)MathSciNetzbMATHGoogle Scholar
  99. 99.
    Gordeziani, D., Gordeziani, N.: On application of decomposition method to solution of initial-boundary value problems for nonlinear parabolic equations with mixed derivatives. Rep. Enlarged Sess. Semin. I. Vekua. Appl. Math. 22, 20–27 (1993)Google Scholar
  100. 100.
    Gordeziani, D., Gordeziani, N.: On investigation of one problem in linear theory of the elastic mixtures. Rep. Enlarged Sess. Semin. I. Vekua. Appl. Math. 22, 108–115 (1993)Google Scholar
  101. 101.
    Gordeziani, D., Gordeziani, N.: On the solution of dynamical problems in the linear theory of elastic mixtures. Appl. Math. Inform. 1(1), 70–77 (1996)MathSciNetzbMATHGoogle Scholar
  102. 102.
    Gordeziani, D., Gordeziani, E.: On investigation of difference schemes for some pluriparabolic equations. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 14(3), 53–57 (1999)MathSciNetzbMATHGoogle Scholar
  103. 103.
    Gordeziani, D., Gordeziani, E.: Difference schemes for pluriparabolic equations. Bull TICMI 4, 41–46 (2000)zbMATHGoogle Scholar
  104. 104.
    Gordeziani, D., Gordeziani, N., Avalishvili, G.: On one class of nonlocal problems for partial differential equations. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 10(3), 20–22 (1995)zbMATHGoogle Scholar
  105. 105.
    Gordeziani, D., Gordeziani, N., Avalishvili, G.: Nonlocal boundary value problems for some partial differential equations. Bull. Georgian Acad. Sci. 157(3), 365–368 (1998)MathSciNetzbMATHGoogle Scholar
  106. 106.
    Gordeziani, D., Gordeziani, E., Gordeziani, N.: On finite-difference methods developed for solution of one Pluri-Schrödinger equation. Bull. Georgian Natl. Acad. Sci. January-February 173(1), 14–17 (2006)zbMATHGoogle Scholar
  107. 107.
    Gordeziani, D., Gordeziani, E., Gordeziani, N.: On finite-difference methods developed for solutions of one pluri-Schrödinger equation. Bull. Georgian Natl. Acad. Sci. 173(1), 14–16 (2006)MathSciNetzbMATHGoogle Scholar
  108. 108.
    Gordeziani, D., Gordeziani, E., Gordeziani, N.: On solution of some initial-boundary value problems for pluri-Schrödinger equation. Bull. Georgian Natl. Acad. Sci. 173(3), 432–434 (2006)MathSciNetzbMATHGoogle Scholar
  109. 109.
    Gordeziani, D.G., Grigalashvili, Z.J.: Nonlocal problems in time for some equations of mathematical physics. Rep. Enlarged Sess. Semin. I. Vekua. Appl. Math. 22, 102–108 (1993)Google Scholar
  110. 110.
    Gordeziani, D., Grigalashvili, Z.: Nonlocal problems in time for some equations of mathematical physics. Dokl. Semin. Inst. Prikl. Mat. im. I.N. Vekua 22, 108–114 (1993)Google Scholar
  111. 111.
    Gordeziani, D.G., Gunava, G.V., Komurdzhishvili, O.P.: Okroashvili T.G., On the numerical modeling of the stress-deformed state of a power plant (Russian). Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 40, 25–33 (1990)zbMATHGoogle Scholar
  112. 112.
    Gordeziani, D.G., Komurdžišvili, O.: The difference scheme for the solution of the first boundary value problem for the equations of a prismatic shell in a curvilinear region (Russian). Studies of certain equations of mathematical physics (Russian). Izdat. Tbilis. Univ., Tbilisi 1, 97–104 (1972)Google Scholar
  113. 113.
    Gordeziani, D.G., Komurdžišvili, O.: The numerical solution of a certain variant of the equations of the theory of thin shells (Russian). Sakharth. SSR, Mecn. Akad. Moambe 67, 533–536 (1972)MathSciNetGoogle Scholar
  114. 114.
    Gordeziani, D.G., Korshiya, T.K., Lobzhanidze, G.B.: Averaged schemes of summary approximation for nonlinear parabolic equations (Russian) Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 18, 68–94 (1986)MathSciNetzbMATHGoogle Scholar
  115. 115.
    Gordeziani, D., Kupreishvili, M., Meladze, H., Davitashvili, T.: On the solution of boundary value problems for differential equations given in graphs. Appl. Math. Inform. Mech. 13(2), 80–91 (2008)MathSciNetzbMATHGoogle Scholar
  116. 116.
    Gordeziani, D.G., Meladze, G.V.: The modelling of multidimensional quasilinear equations of parabolic type by one-dimensional equations (Russian). Sakharth SSR, Mecn. Akad. Moambe 60, 537–540 (1970)MathSciNetzbMATHGoogle Scholar
  117. 117.
    Gordeziani, D.G., Meladze, H.V.: The simulation of the third boundary value problem for multidimensional parabolic equations in an arbitrary domain by one-dimensional equations (Russian). Ž. Vyčisl. Mat. i Mat. Fiz. 14, 246–250 (1974)MathSciNetGoogle Scholar
  118. 118.
    Gordeziani, D., Meladze, I.: Nonlocal contact problem for two-dimensional linier elliptic equations. Bull. Georgian Acad. Sci. 8(1), 61–64 (2014)zbMATHGoogle Scholar
  119. 119.
    Gordeziani, D., Meladze, I.: Nonlocal contact problem for two-dimensional linear elliptic equations. Bull. Georgian Natl. Acad. Sci. (N.S.) 8(1), 40–50 (2014)MathSciNetzbMATHGoogle Scholar
  120. 120.
    Gordeziani, D., Meladze, H., Avalishvili, G.: On one class of nonlocal in time problems for first-order evolution equations. J. Comp. and Appl. Math. 88(1), 66–78 (2003)zbMATHGoogle Scholar
  121. 121.
    Gordeziani, D.G., Meladze, H.V., Davitashvili, T.D.: On one generalization of boundary value problems for ordinary differential equations on graphs in the three-dimensional space. WSEAS Trans. Math. 8(8), 457–466 (2009)MathSciNetGoogle Scholar
  122. 122.
    Gordeziani, D., Shapatava, A.: On regularized difference scheme for one quasilinear parabolic equation. Appl. Math. Inform. 5(2), 70–77 (2000)MathSciNetzbMATHGoogle Scholar
  123. 123.
    Gordeziani, D.G., Zizova, L.A., Komurdžišvili, O., Meladze, G.V.: Difference methods for the calculation of a certain version of the equations of the theory of thin shells, in Coll (Russian). Stud. Certain Equ. Math. Phys. 1, 87–96 (1972)Google Scholar
  124. 124.
    Kachiashvili K.J., Gordeziani D.G., Melikdzhanian D.I.: Both deterministic and stochastic mathematical models of river water pollution level control and management and their realization as applied program package. Thesis of Reports of VI\({}^{th}\) International Congress of Hydrologists, St. Petersburg, Russia pp. 141–143 (2004)Google Scholar
  125. 125.
    Kachiashvili K.J., Gordeziani D.G., Melikdzhanian D.I.: Software realization problems of mathematical models of pollutants transport in rivers. In: ISAAC Conference on Complex Analysis, Partial Differential Equations and Mechanics of Continua, Tbilisi, pp. 9–10 (2007)Google Scholar
  126. 126.
    Kachiashvili, K.J., Gordeziani, D.G., et al.: Software packages for automation of environmental monitoring and experimental data processing. In: 3-th International Conference “Advances of Computer Methods in Geotechnical and Geoenvironmental Engineering”, Moscow, pp. 273–278 (2000)Google Scholar
  127. 127.
    Kachiashvili, K.J., Gordeziani, D.G., Melikdzhanian, D.I.: Mathematical models of dissemination of pollutants with allowance for of many sources of effect. In: Proceedings of the Urban Drainage Modeling Symposium, vol. 6, pp. 692–702. Orlando, Florida (2001)Google Scholar
  128. 128.
    Kachiashvili, K.J., Gordeziani, D.G., Lazarov, R.G., Melikdzhanian, D.I.: Modeling and simulation of pollutants transport in rivers. Int. J. Appl. Math. Model. (AMM) 31, 1371–1396 (2007)zbMATHCrossRefGoogle Scholar
  129. 129.
    Kachiashvili, K.J., Gordeziani, D.G., Melikdzhanian, D.I.: Mathematical Models, Methods and Algorithms of Control and Regulation of Water Quality in Rivers. Georgian Technical University, Tbilisi (2007)zbMATHGoogle Scholar
  130. 130.
    Kachiashvili, K.J., Gordeziani, D.G., Melikdzhanian, D.I., Nakani, D.V.: River pollution components mean annual values estimation by computer modeling. AMIM 11(1), 20–30 (2006)zbMATHGoogle Scholar
  131. 131.
    Kachiashvili, K.J., Gordeziani, D.G., Melikdzhanian, D.I., Stepanishvili, V.A.: Packages of the applied programs for the solution of problems of ecology and processing of the experimental data. Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of. Appl. Math. 17(3), 97–100 (2002)Google Scholar
  132. 132.
    Papukashvili, A., Gordeziani, D., Davitashvili, T., Sharikadze, M.: On finite-difference method for approximate solution of antiplane problems of elasticity theory for composite bodies weakened by cracks. Rep. Enlarged Sess. Semin. I. Vekua Inst. Appl. Math. 27(3), 42–45 (2013)Google Scholar
  133. 133.
    Papukashvili, A., Gordeziani, D., Davitashvili, T.: Some questions of approximate solutions for composite bodies weakened by cracks in the case of antiplanar problems of elasticity theory. Appl. Math. Inform. Mech. 15(2), 33–43 (2010)MathSciNetGoogle Scholar
  134. 134.
    Papukashvili, A., Gordeziani, D., Davitashvili, T., Sharikadze, M.: On one method of approximate solution of antiplane problems of elasticity theory for composite bodies weakned by cracks. Rep. Enlarged Sess. Semin. I. Vekua Inst. Appl. Math. 26, 50–53 (2012)zbMATHGoogle Scholar
  135. 135.
    Papukashvili, A., Gordeziani, D., Davitashvili, T., Sharikadze, M., Manelidze, G., Kurdghelashvili, G.: About methods of approximate solutions for composite bodies weakened by cracks in the case of antiplane problems of elasticity theory. Appl. Math. Inform. Mech. 16(1), 49–55 (2011)MathSciNetGoogle Scholar

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Authors and Affiliations

  1. 1.I.Vekua Institute of Applied Mathematics of I.Javakhishvili Tbilisi State UniversityTbilisiGeorgia
  2. 2.Georgian Technical UniversityTbilisiGeorgia

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