Quasilinear parabolic problem with variable exponent: Qualitative analysis and stabilization

被引：25

作者：

Giacomoni, Jacques ^{[1
]}

Radulescu, Vicentiu ^{[2
,3
]}

Warnault, Guillaume ^{[4
]}

机构：

[1] Univ Pau & Pays Adour, Lab Math & Leurs Applicat Pau, UMR CNRS 5142, Ave Univ,BP 1155, F-64013 Pau, France

[2] King Abdulaziz Univ, Fac Sci, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia

[3] Univ Craiova, Dept Math, St AI Cuza 13, Craiova 200585, Romania

[4] Univ Pau & Pays Adour, Lab Math & Leurs Appl Pau, UMR CNRS 5142, Ave Univ,BP 1155, F-64013 Pau, France

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2018年 / 20卷 / 08期

关键词：

Leray-Lions operator with variable exponents; parabolic equation; local and global in time existence; stabilization; EIGENVALUE PROBLEM; EQUATIONS; EXISTENCE; REGULARITY; UNIQUENESS;

D O I：

10.1142/S0219199717500651

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss the existence and uniqueness of the weak solution of the following nonlinear parabolic problem: (P-T) {u(t) - del . a(x, del u) = f(x,u) in Q(T) =(def) (0, T) x Omega, u = 0 on Sigma(T) =(def) (0, T) x partial derivative Omega, u(0,x) = u(0)(x) in Omega, which involves a quasilinear elliptic operator of Leray-Lions type with variable exponents. Next, we discuss the global behavior of solutions and in particular the convergence to a stationary solution as t -> infinity.

引用

页数：38

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