Differential Equations

, Volume 55, Issue 5, pp 658–668 | Cite as

Uniqueness of Solution of the First Initial-Boundary Value Problem for Parabolic Systems with Constant Coefficients in a Semibounded Domain on the Plane

  • E. A. BaderkoEmail author
  • M. F. CherepovaEmail author
Partial Differential Equations


The first initial-boundary value problem is considered for a Petrovskii parabolic second-order system with constant coefficients in a semibounded domain with nonsmooth lateral boundary on the plane. The uniqueness of solution of this problem in Holder classes is proved.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Maz’ya, V.G. and Kresin, G.I., On the maximum principle for strongly elliptic and parabolic second order systems with constant coefficients, Math. USSR Sb., 1986, vol. 53, no. 2, pp. 457–479.CrossRefzbMATHGoogle Scholar
  2. 2.
    Solonnikov, V.A., On boundary value problems for linear parabolic systems of differential equations of general form, Proc. Steklov Inst. Math., 1965, vol. 83, pp. 1–184.MathSciNetGoogle Scholar
  3. 3.
    Ladyzhenskaya, O.A., Solonnikov, V.A., and Ural’tseva, N.N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa (Linear and Quasilinear Equations of Parabolic Type), Moscow: Nauka, 1967.Google Scholar
  4. 4.
    Baderko, E.A. and Cherepova, M.F., The first boundary value problem for parabolic systems in plane domains with nonsmooth lateral boundaries, Dokl. Math., 2014, vol. 90, no. 2, pp. 573–575.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Baderko, E.A. and Cherepova, M.F., Simple layer potential and the first boundary value problem for a parabolic system on the plane, Differ. Equations, 2016, vol. 52, no. 2, pp. 197–209.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Baderko, E.A. and Cherepova, M.F., Smoothness in the Dini space of a single layer potential for a parabolic system in the plane, J. Math. Sci., 2018, vol. 235, no. 2, pp. 154–167.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Baderko, E.A. and Cherepova, M.F., Uniqueness of solution to the first initial boundary value problem for parabolic systems on the plane in a model case, Dokl. Math., 2018, vol. 98, no. 3, pp. 579–581.CrossRefzbMATHGoogle Scholar
  8. 8.
    Petrovskii, I.G., On the Cauchy problem for systems of linear partial differential equations in the domain of nonanalytic functions, Byull. Mosk. Gos. Univ. Sect. A, 1938, vol. 1, no. 7, pp. 1–72.Google Scholar
  9. 9.
    Eidel’man, S.D., Parabolicheskie sistemy (Parabolic Systems), Moscow: Nauka, 1964.Google Scholar
  10. 10.
    Friedman, A., Partial Differential Equations of Parabolic Type, Englewood Cliffs: Prentice-Hall, 1964. Translated under the title Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Moscow: Mir, 1968.zbMATHGoogle Scholar
  11. 11.
    Tveritinov, V.A., Gladkost’ potentsiala prostogo sloya dlya parabolicheskoi sistemy vtorogo poryadka (Smoothness of the Simple Layer Potential for a Second-Order Parabolic System), Available from VINITI, 1988, no. 6850-V88.Google Scholar
  12. 12.
    Semaan, Kh.M., Ob otsenkakh v prostranstvakh Gel’dera starshei proizvodnoi potentsiala prostogo sloya dlya parabolicheskikh sistem s odnoi prostranstvennoi peremennoi (On Estimates in Hölder spaces for the Highest Derivative of the Simple Layer Potential for Parabolic Systems with One Spatial Variable), Available from VINITI, 1998, no. 927-V98.Google Scholar
  13. 13.
    Vladimirov, V.S., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1981.Google Scholar
  14. 14.
    Cherepova, M.F., On the smoothness of the volume mass potential for parabolic systems, Vestn. Mosk. Energ. Inst., 1999, no. 6, pp. 86–97.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.National Research University “Moscow Power Engineering Institute”MoscowRussia

Personalised recommendations