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.
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页码：183 / 236
页数：54
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