EXISTENCE AND DECAY OF SOLUTIONS TO COUPLED SYSTEMS OF NONLINEAR WAVE EQUATIONS WITH VARIABLE EXPONENTS

被引：2

作者：

Bouhoufani, Oulia ^{[1
]}

Messaoudi, Salim A. ^{[2
]}

Zahri, Mostafa ^{[2
]}

机构：

[1] Univ Batna 2, Dept Math, Batna 05000, Algeria

[2] Univ Sharjah, Dept Math, POB 27272, Sharjah, U Arab Emirates

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 2023卷 / 73期

关键词：

Coupled system; hyperbolic equation; existence; energy decay; variable-exponent; time-dependent coefficients; BLOW-UP; SPACES;

D O I：

10.58997/ejde.2023.73

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider a coupled system of two hyperbolic equations with variable exponents in the damping and source terms, where the dampings are modilated with time-dependent coefficients alpha(t), 0(t). First, we state and prove an existence result of a global weak solution, using Galerkin's method with compactness arguments. Then, by a Lemma due to Martinez, we establish the decay rates of the solution energy, under suitable assumptions on the variable exponents m and r and the coefficients alpha and 0. To illustrate our theoretical results, we give some numerical examples.

引用

页数：20

共 29 条

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