Existence and non-existence of global solutions of the Cauchy problem for higher order semilinear pseudo-hyperbolic equations

被引：25

作者：

Aliev, Akbar B. ^{[1
]}

Lichaei, Bijan H. ^{[1
]}

机构：

[1] Azerbaijan Tech Univ, Inst Math & Mech, NAS Azerbaijan, AZ-1141 Baku, Azerbaijan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 7-8期

关键词：

Cauchy problem; Pseudo-hyperbolic; Semilinear; Existence; Non-existence; Global solution; DISSIPATIVE WAVE-EQUATIONS; BLOW-UP; ASYMPTOTIC-BEHAVIOR; DECAY;

D O I：

10.1016/j.na.2009.12.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for a higher order pseudo-hyperbolic equation. Using the L-p -> L-q type estimation for the corresponding linear problem, the existence and nonexistence criteria of global solutions are found. The existence and uniqueness of smooth global solutions are also investigated. We also establish the behavior of solutions and their derivatives as t -> +infinity. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：3275 / 3288

页数：14

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