GLOBAL EXISTENCE AND GENERAL DECAY OF SOLUTION FOR A NONLINEAR WAVE EQUATION WITH VARIABLE EXPONENTS AND MEMORY TERM

被引：0

作者：

Boughamsa, Wissem ^{[1
]}

Ouaoua, Amar ^{[1
]}

机构：

[1] Univ 20 August 1955, LAMAHIS Lab, Skikda, Algeria

来源：

MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS | 2023年 / 89卷

关键词：

Wave equation; variable exponents; memory term; global existence; general decay; BLOW-UP; ASYMPTOTIC STABILITY; PARABOLIC EQUATION; SOBOLEV EMBEDDINGS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the following wave equation: u(tt) -Delta u - Delta u(tt) + (0)integral(t) g(t-s)Delta u(s)ds + |u(t) |(m(x)-2) u(t) = b |u|(p(x)-2) u. First, we prove that the equation has a unique local solution for a suitable conditions by using Faedo-Galerkin methods, and we also prove that the local solution is global in time. Finally, we demonstrate that the solution with positive initial energy decays exponentially.

引用

页码：61 / 78

页数：18

共 25 条

[1] Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain [J].