Abstract
In the current work there are shortly described several methods and prospective directions of mathematical and numerical modelling, that seem very promising and efficient for further application and investigation of problems of water and air quality control in water bodies and the atmosphere, respectively. Namely, for certain linear non-classical problems issues of existence and uniqueness, finite-difference are investigated and decomposition methods are developed for their solution.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A.V.B. Karaushev, River Hydraulic, Hydro-meteorological Edition, Leningrad, 1969, p. 415.
G.I. Marchuk, Mathematical Modelling in Environmental Problem, M.J. Nauka, 1982, p. 319.
A.M. Nikanorov, N.M. Trunov, Internal Processes in Reservoirs and Quality Control of Natural Waters, Under the Edition of A.I. Bedritskii, Sankt-Peterburg, GIDROMETEOIZDAT, 1999, p. 155.
A.A. Samarskii, Introduction to Theory of Finite Difference Schemes, Naukam 1971.
A.A. Samarskii, Theory of Finite Difference Schemes, Moskva, Nauka, 1977.
A. Fridman, Partial Differential Equations of Parabolic Type, Edition Mir, 1968, p. 420.
A.N. Tikhonov, A.A. Samarskii, Equations of Mathematical Physics, Edit. “Nauka”, Main Edition of Physical-Mathematical Literature, Moscw, 1977.
A.A. Samarskii, On One Economic Difference Method of Solution of Multi-Dimensional Parabolic Equation in Arbitrary Area, JAM and MPh, 1962, vol. 2, 5, pp. 787–811.
B. Samarskyi and A. Gulin, Numerical Methods,-Moscow, Nauka, 1989, p. 430.
J. Brandt, I. Dimov, K. Georgiev, I. Uzia, Z. Zlatev, Numerical Algorithms for Threedimensional Version of the Danish Eulerian Model, Regional Modelling of Air pollution in Europe Proceedings of the first REMAPE Workshop, Copenhagen, Denmark, 1996, pp. 250–262.
A.V. Karaushev, Hydraulic of Rivers and Water Reservoirs, River Transport Edition, Leningrad, 1955.
E. Gordeziani, On numerical methods for the resolution of one non-classical problem with pluri-parabolic equation, Proceedings of I. Vekua Institute of Applied Mathematics, Tbilisi State University Press, 50–51, 2000–2001, pp. 38–47.
E. Gordeziani, D. Gordeziani, Difference schemes for pluriparabolic equations, Bulletin of TICMI, Tbilisi University Press, Vol. 4, 2000, pp. 41–46.
J.R. Cannon, The solution of the heat equation subject to the specification of energy, Quart. Applied Mathematics 21, 1963, pp. 155–160.
R. Dautray, J.-L. Lions. Analyse mathématique et calcul numérique pour les science et les techniques. Vol. 7, Évolution: Fourier, Laplace, MASSON, Paris, Milan, Barcelona, Mexico, 1988, pp. 187–200.
N.D. Gordeziani, On the Resolution of Non-local Boundary-value Problems for Elliptic Equations, Seminar of Vekua Institute of Applied Mathematics, Reports, vol. 23, 1997, pp. 26–35.
D. Gordeziani, N. Gordeziani, G. Avalishvili, On One Class of Non-local Problems for Partial Differential Equations, Reports of Enlarged Session of the Seminar of Vekua Institute of Applied Mathematics, vol. 10, #3, 1995, pp. 13–16.
D. Gordeziani, N. Gordeziani, G. Avalishvili, Non-local Boundary-value Problems for Some Partial Differential Equations, Bulletin of the Georgian Academy of Sciences, 157, #1, 1998, pp. 365–369.
E. Gordeziani, N. Gordeziani, On Some Generalization of Non-local Boundary Value Problems for Elliptic Equations, Bulletin of TICMI, Tbilisi University Press, Vol. 2, 1998, pp. 34–36.
E. Gordeziani, D. Gordeziani, On Investigation of Difference Schemes for Some Pluriparabolic Equations, Reports of enlarged sessions of the seminars of I. Vekua Instutute of Applied Mathematics, Tbilisi University Press, Vol. 14, # 3, 1999, pp. 53–57.
E.D. Gordeziani, H.V. Meladze, On Investigation of One Non-classical Initial Boundary Value Problem, Third International Conference Finite Difference Schemes (FDS), September 1–4. 2000, Palanga, Lithunia, Abstracts, p. 18.
E.D. Gordeziani, H.V. Meladze, F.C. Torralba, On Mathematical Modelling and Numerical Resolution of Pollution Diffusion in Rivers, Proceedings of the third international conference on advances of computer methods in geotechnical and geoenvironmental engineering, Geoecology and Computers, Edited by Sergey A. Yufin, Center of Underground and Special Engineering, Moscow State University of Civil Engineering, Moscow/Russia/1–4 February, A.A. Balkema/Rotterdam/-Prookfield/2000, pp. 509–511.
E. Gordeziani, On Investigation of Non-local Problem for Certain Elliptic Equation, Proceedings of I. Vekua Institute of Applied Mathematics, Tbilisi State University Press, 50–51, 2000–2001, pp. 48–57.
N. Gordeziani, Non-local in Time Problems in the Theory of Elasticity, Reports of Enlarged Session of the Seminar of Vekua Institute of Applied Mathematics, vol.14, #3, 1999, pp. 16–20.
D. Gordeziani, N. Gordeziani, G. Avalishvili, Non-local Boundary-value Problems in Mathematical Physics. Abstract, Differential Equations and Mathematical Physics, International Symposium dedicated to the 90-th Birthday Anniversary of Academician I. Vekua, Tbilisi, 1997, pp. 127–128.
N. Gordeziani, On Some Non-local Problems of the theory of elasticity. Tbilisi International Centre of Mathematics and Informatics, BULLETIN of TICMI, Volume 4, 2000, pp. 43–47.
D.G. Gordeziani, On resolution of non-local by time problems for some equations of mathematical physics, ICM-94, Abstracts, Short communication, 1994, p. 240.
A.V. Bitsadze., A.A. Samarskii, On Some Generalization of Linear Elliptic Equations, DAN SSSR, 1969, vol. 185, #4, pp. 739–740.
A. M. Il’in, On a certain class of ultraparabolic equations, DAN SSSR. 159, No. 6, 1964, pp. 1214–1217.
D. Gordeziani, N. Gordeziani, G. Avalishvili, On the Investigation and Resolution of Non-local Boundary and Initial-boundary Value Problems, Reports of Enlarged Session of the Seminar of Vekua Institute of Applied Mathematics, vol. 12, #3, 1997, pp. 20–23.
A. Bouziani, Strong solution for a mixed problem with non-local condition for certain pluriparabolic equations Hiroshima Math. J., 1997, vol. 27, pp. 373–390.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
GORDEZIANI, D., GORDEZIANI, E. (2007). MATHEMATICAL MODELLING AND NUMERICAL SOLUTION OF SOME PROBLEMS OF WATER AND ATMOSPHERE POLLUTION. In: Ebel, A., Davitashvili, T. (eds) Air, Water and Soil Quality Modelling for Risk and Impact Assessment. NATO Security Through Science Series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5877-6_18
Download citation
DOI: https://doi.org/10.1007/978-1-4020-5877-6_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-5875-2
Online ISBN: 978-1-4020-5877-6
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)