Optimal decay rate of the energy for wave equations with critical potential

被引：40

作者：

Ikehata, Ryo ^{[1
]}

Todorova, Grozdena ^{[2
]}

Yordanov, Borislav ^{[2
]}

机构：

[1] Hiroshima Univ, Grad Sch Educ, Dept Math, Higashihiroshima 7398524, Japan

[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2013年 / 65卷 / 01期

基金：

日本学术振兴会;

关键词：

damped wave equation; critical potential; energy decay; finite speed of propagation; diffusive structure; TIME-DEPENDENT DISSIPATION; ASYMPTOTIC-BEHAVIOR; CRITICAL EXPONENT; SPACE;

D O I：

10.2969/jmsj/06510183

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the long time behavior of solutions of the wave equation with a variable damping term V(x)u(t) in the case of critical decay V(x) >= V-0(1 + vertical bar x vertical bar(2))(-1/2) (see condition (A) below). The solutions manifest a new threshold effect with respect to the size of the coefficient V-0: for 1 < V-0 < N the energy decay rate is exactly t(-V0), while for V-0 >= N the energy decay rate coincides with the decay rate of the corresponding parabolic problem.

引用

页码：183 / 236

页数：54

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