Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations

被引：65
作者：
Ono, K [1 ]
机构：
[1] Univ Tokushima, Dept Math & Nat Sci, Tokushima 7708502, Japan
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2003年 / 9卷 / 03期
关键词：
dissipative wave equation; critical exponent; global existence; asymptotic behavior; decay rate;
D O I：
10.3934/dcds.2003.9.651
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the global existence and asymptotic behavior of solutions to the Cauchy problem for the semilinear dissipative wave equations : squareu + partial derivative(t)u = \u\(alpha+1), u\(t=0) = epsilonu(o) is an element of H-1 boolean AND L-1, partial derivative(t)u\(t=o) = epsilonu(1) is an element of L-2 boolean AND L-1 with a small parameter epsilon > 0. When N less than or equal to 3 and 2/N < α ≤ 2/[N - 2](+), we show the global solvability and derive the sharp rates of the solutions.
引用
收藏
页码：651 / 662
页数：12
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