GLOBAL SOLUTIONS AND FINITE TIME BLOW UP FOR DAMPED KLEIN-GORDON EQUATION

We study the Cauchy problem of strongly damped Klein-Gordon equation. Global existence and asymptotic behavior of solutions with initial data in the potential well are derived. Moreover, not only does finite time blow up with initial data in the unstable set is proved, but also blow up results with...

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Bibliographic Details
Published inActa mathematica scientia Vol. 33; no. 3; pp. 643 - 652
Main Author 徐润章 丁云华
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.05.2013
College of Science, Harbin Engineering University, Harbin 150001, China
Subjects
35A01
35B40
35B44
Asymptotic properties
blow up
Cauchy problem
global solutions
Klein-Gordon equation
Klein-Gordon方程
Mathematical analysis
strongly damped
不稳定集
强阻尼
整体存在性
整体解
有限时间
柯西问题
爆破
global solutions
Klein-Gordon equation
35A01
35B44
blow up
35B40
strongly damped
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ISSN0252-9602
1572-9087
DOI10.1016/S0252-9602(13)60027-2

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Summary:We study the Cauchy problem of strongly damped Klein-Gordon equation. Global existence and asymptotic behavior of solutions with initial data in the potential well are derived. Moreover, not only does finite time blow up with initial data in the unstable set is proved, but also blow up results with arbitrary positive initial energy are obtained.
Bibliography:Klein-Gordon equation; strongly damped; global solutions; blow up
Runzhang XU Yunhua DING（College of Science, Harbin Engineering University, Harbin 150001, China）
42-1227/O
We study the Cauchy problem of strongly damped Klein-Gordon equation. Global existence and asymptotic behavior of solutions with initial data in the potential well are derived. Moreover, not only does finite time blow up with initial data in the unstable set is proved, but also blow up results with arbitrary positive initial energy are obtained.
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(13)60027-2