Polynomial Decay and Blow Up of Solutions for Variable Coefficients Viscoelastic Wave Equation with Acoustic Boundary Conditions

被引：26

作者：

Boukhatem, Yamna ^{[1
]}

Benabderrahmane, Benyattou ^{[2
]}

机构：

[1] Univ Laghouat, Fac Sci, Lab Comp Sci & Math, POB 37G, Laghouat 03000, Algeria

[2] Univ MSila, Fac Math & Comp Sci, Msila, Algeria

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2016年 / 32卷 / 02期

关键词：

Acoustic boundary conditions; blow up; polynomial decay; variable coefficients; viscoelastic; wave equation; EXISTENCE; OBSERVABILITY; ENERGY;

D O I：

10.1007/s10114-016-5093-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A variable coefficient viscoelastic wave equation with acoustic boundary conditions and nonlinear source term is considered. Under suitable conditions on the initial data and the relaxation function g, we show the polynomial decay of the energy solution and the blow up of solutions by energy methods. The estimates for the lifespan of solutions are also given.

引用

页码：153 / 174

页数：22

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