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

页码：651 / 662

页数：12

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