THE SOLVABILITY OF BOUNDARY VALUE PROBLEM
FOR NONLINEAR ELLIPTIC-PARABOLIC EQUATIONS

Abstract

The nonlinear elliptic-parabolic equations of nondivergent structure is considered. The solvability of the boundary value problems is investigated.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 3
Year: 2021

DOI: 10.12732/ijam.v34i3.7

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References

  1. [1] M.V. Keldysh, On some cases of degeneration of an equation of elliptic type on the domain boundary, Dokl. Akad. Nauk SSSR, 77, No 2 (1951), 181-183.
  2. [2] G. Fichera, On a unified theory of boundary value problems for ellipticparabolic equations of second order, Matematika, 7, No 6 (1963), 99-122.
  3. [3] O.A. Oleynik, J.V. Radkevitch, Second order quations with nonnegative characteristic form, VINITI, Ser. Itogi Nauki, Math. Analysis (1971), 7- 252.
  4. [4] M. Franciosi, Sul de un equazioni elliptico-parabolica a coefficienti discontinue, Boll. Un. Math. Ital., 6, No 2 (1983), 63-75.
  5. [5] M. Franciosi, Un theoreme di esistenza ed unicita per la soluzione di un’equazione elliptico-parabolica, a coefficienti-discontinui, in forma non divergenza, Bull. Un. Mat. Ital., 6, No 4-B (1985), 253-263.
  6. [6] A. Alvino, G.Trombetti, Second order elliptic equation whose coefficients have their first derivatives weakly-Ln, Annali di Matematica Pura ed Applicata , 138 (1984), 331-340.
  7. [7] T.S. Gadjiev, E. Gasimova, On smoothness of solution of the first boundary-value problem for second order degenerate elliptic-parabolic equations, Ukranian Mathematical Journal, 60, No 6 (2008), 723-736.
  8. [8] S. Chanillo, R.L. Wheeden, Existence and estimates of Green’s function for degenerate elliptic equations, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 15, No 2 (1988), 309-340.
  9. [9] P.A. Domenico, F.W. Schwartz, Physical and Chemical Hydrogeology, John Wiley and Sons, New York (1998).
  10. [10] W.Merza, P. Rybka, Strong solutions to the Richards equation in the unsaturated zone, Journal of Mathematical Analysis and Applications, 371, No 2 (2010), 741-749.
  11. [11] T.S. Gadjiev, A.V. Mammadova, Regularity of solutions of classes nonlinear elliptic-parabolic problems, Spectral Theory and its Applications, Baku (2019), 68-70.
  12. [12] T.S. Gadjiev, M.N. Kerimova, G. Gasanova, The solvability of boundary value problem for degenerate equations, Ukranian Mathematical Journal 4 (2020), to appear.
  13. [13] T.S. Gadjiev, S.Y. Aliev, M.N. Kerimova, The strong solvability boundary value problem for linear non-divergent degenerate equations of ellipticparabolic type, Proceedings of IAM, 8, No 1 (2019), 14-23.