THE SMOOTHNESS OF SOLUTIONS OF
DEGENERATE NONLINEAR ELLIPTIC EQUATIONS
Gulnara Zulfaliyeva
Institute of Mathematics and Mechanics
Azerbaijan National Academy of Science
Baku, AZERBAIJAN

Abstract

We are investigated initial-boundary value problem for degenerate nonlinear elliptic-parabolic equations. This problem is connected with the nonlinear reaction, drift, diffusion processes which arise as mathematical models of different problems of applied sciences. The problem is considered under standard conditions for the coefficients and some conditions for the weight functions. The qualitative property of the solution 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: 35
Issue: 1
Year: 2022

DOI: 10.12732/ijam.v35i1.4

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References

  1. [1] M.V. Keldysh, On some cases of degeneration of equations of elliptic type on the boundary of a domain, DAN SSSR, 77, No 2 (1951), 181-183.
  2. [2] G. Fichera, On a unified theory of boundary value problem for ellipticparabolic equations of second order. In: Boundary Problems in Differential Equations, Madison, 1960, 97-120.
  3. [3] T. Gadjiev, M. Kerimova, The solutions degenerate elliptic-parabolic equations, J. of Advances in Mathematics, 3, No 3 (2013), 219-235.
  4. [4] P.H. Benilan, P.Wittbold, On mild and weak solutions of elliptic-parabolic systems, Adv. Differ. Equ., 1 (1996), 1053-1073.
  5. [5] T.S. Gadjiev, E.R. Gasimova, On smoothness of solution of the first boundary-value problem for second order degenerate elliptic-parabolic equations, Ukrainian Math. J., 60, No 6 (2008), 723-736.
  6. [6] H. Gajewski, I.V. Skrypnik, To the uniqueness problem for nonllinear elliptic equations, Nonlin. Analysis, 52 (2003), 291-304.
  7. [7] S. Chanillo, R. Wheeden, Weighted Poincare and Sobolev inequalities, Amer. J. Math., 107 (1985), 1191-1226.
  8. [8] M.N. Karimova, The estimation of solutions nondivergent elliptic-parabolic equations, Intern. J. of Appl. Math., 32, No 5 (2019), 759-767; DOI: 10.12732/ijam.v32i5.3.
  9. [9] T. Gadjiev, M. Kerimova, G. Gasanova, Solvability of a boundary-value problem for degenerate equations, Ukrainian Math. J., 72, No 4 (2020), 495-514.