Existence and decay results for a von Karman equation with variable exponent nonlinearities

被引：4

作者：

Ha, Tae Gab ^{[1
,2
]}

Park, Sun-Hye ^{[3
]}

机构：

[1] Jeonbuk Natl Univ, Dept Math, Jeonju, South Korea

[2] Jeonbuk Natl Univ, Inst Pure & Appl Math, Jeonju, South Korea

[3] Pusan Natl Univ, Off Educ Accreditat, Busan 46241, South Korea

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 11期

基金：

新加坡国家研究基金会;

关键词：

existence of solution; stability; variable exponent; von Karman equation;

D O I：

10.1002/mma.7372

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider a von Karman equation with variable exponent nonlinearities w(tt)(x, t) + Delta(2)w(x, t) + vertical bar w(t)(x, t)vertical bar gamma((x)-2)w(t)(x, t) = [w(x, t), F(w(x, t))] + vertical bar w(x, t)vertical bar(p(x)-2)w(x, t) in a bounded domain Omega subset of R-2. We firstly discuss an existence result of solutions by utilizing Faedo-Galerkin approximation technique. Then, we undertake an investigation of asymptotic stability to the solutions by making use of the multiplier method.

引用

页码：9475 / 9486

页数：12

共 28 条

[1] New diffusion models in image processing [J].

Aboulaich, R. ;

Meskine, D. ;

Souissi, A. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (04) :874-882

[2]

Adams RA., 2003, Sobolev Space, V2

[3]

[Anonymous], 2015, ATLANTIS STUDIES DIF

[4] WAVE EQUATION WITH p(x,t)-LAPLACIAN AND DAMPING TERM: EXISTENCE AND BLOW-UP [J].

Antontsev, Stanislav .

DIFFERENTIAL EQUATIONS & APPLICATIONS, 2011, 3 (04) :503-525

[5] GLOBAL DECAY-RATES FOR THE SOLUTIONS TO A VONKARMAN PLATE WITHOUT GEOMETRIC CONDITIONS [J].

BRADLEY, ME ;

LASIECKA, I .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1994, 181 (01) :254-276

[6] Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term [J].

Cavalcanti, MM ;

Cavalcanti, VND ;

Martinez, P .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 203 (01) :119-158

[7]

Chueshov I, 2010, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-0-387-87712-9

[8] Lebesgue and Sobolev Spaces with Variable Exponents [J].

Diening, Lars ;

Harjulehto, Petteri ;

Hasto, Peter ;

Ruzicka, Michael .

LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 :1-+

[9] Sobolev embeddings with variable exponent [J].

Edmunds, DE ;

Rákosník, J .

STUDIA MATHEMATICA, 2000, 143 (03) :267-293

[10] On the spaces Lp(x)(Ω) and Wm, p(x)(Ω) [J].

Fan, XL ;

Zhao, D .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 263 (02) :424-446

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