Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces

被引：19
|
作者：
Mukminov, F. Kh. [1 ]
机构：
[1] Russian Acad Sci, Ufa Sci Ctr, Inst Math Comp Ctr, Ufa, Russia
来源：
SBORNIK MATHEMATICS | 2017年 / 208卷 / 08期
基金：
俄罗斯基础研究基金会;
关键词：
anisotropic parabolic equation; renormalized solution; variable nonlinearity; uniqueness of solution; N-function; ENTROPY SOLUTIONS; EXISTENCE; EQUATION; DECAY;
D O I：
10.1070/SM8691
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the first mixed problem for a class of anisotropic elliptic-parabolic equations with double variable nonlinearities in a cylindrical domain (0, T) x Omega. The domain Omega subset of R-n can be unbounded. The uniqueness of the renormalized solution is proved using Kruzhkov's method of doubling the variable t. The same result is established for an equation with non-power law nonlinearities.
引用
收藏
页码：1187 / 1206
页数：20
相关论文
共 50 条
  • [1] On the Entropy Solution to an Elliptic Problem in Anisotropic Sobolev-Orlicz spaces
    Kozhevnikova, L. M.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2017, 57 (03) : 434 - 452
  • [2] Existence of a Renormalized Solution of a Parabolic Problem in Anisotropic Sobolev–Orlicz Spaces
    Vorob’yov N.A.
    Mukminov F.K.
    Journal of Mathematical Sciences, 2021, 258 (1) : 37 - 64
  • [3] Existence and uniqueness of entropy solution of a nonlinear elliptic equation in anisotropic Sobolev-Orlicz space
    Benslimane, Omar
    Aberqi, Ahmed
    Bennouna, Jaouad
    RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2021, 70 (03) : 1579 - 1608
  • [4] On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces
    L. M. Kozhevnikova
    Computational Mathematics and Mathematical Physics, 2017, 57 : 434 - 452
  • [5] ON A SOLUTION OF DEGENERATE ELLIPTIC-PARABOLIC SYSTEMS IN ORLICZ-SOBOLEV SPACES .2.
    KACUR, J
    MATHEMATISCHE ZEITSCHRIFT, 1990, 203 (04) : 569 - 579
  • [6] ON A SOLUTION OF DEGENERATE ELLIPTIC-PARABOLIC SYSTEMS IN ORLICZ-SOBOLEV SPACES-I
    KACUR, J
    MATHEMATISCHE ZEITSCHRIFT, 1990, 203 (01) : 153 - 171
  • [7] Existence of a renormalized solutions for parabolic-elliptic system in anisotropic Orlicz-Sobolev spaces
    Ahakkoud, Y.
    Bennouna, J.
    Elmassoudi, M.
    RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2024, 73 (07) : 2475 - 2500
  • [8] Uniqueness of renormalized solutions of elliptic-parabolic problems
    Carrillo, J
    Wittbold, P
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 328 (01): : 23 - 28
  • [9] Existence and uniqueness of a renormalized solution of parabolic problems in Orlicz spaces
    Abercji, A.
    Bennouna, J.
    Elmassoudi, M.
    Hammoumi, M.
    MONATSHEFTE FUR MATHEMATIK, 2019, 189 (02): : 195 - 219
  • [10] Existence and uniqueness of a renormalized solution of parabolic problems in Orlicz spaces
    A. Aberqi
    J. Bennouna
    M. Elmassoudi
    M. Hammoumi
    Monatshefte für Mathematik, 2019, 189 : 195 - 219
12345