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

doi:10.1016/S0252-9602(13)60027-2

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (3): 643-652.doi: 10.1016/S0252-9602(13)60027-2

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

徐润章|丁云华

College of Science, Harbin Engineering University, Harbin 150001, China

收稿日期:2011-03-21 修回日期:2012-08-04 出版日期:2013-05-20 发布日期:2013-05-20
基金资助:
The first author is supported by the National Natural Science Foundation of China (11101102), Ph.D. Programs Foundation of Ministry of Education of China (20102304120022), the Support Plan for the Young College Academic Backbone of Heilongjiang Province (1252G020), the Natural Science Foundation of Heilongjiang Province (A201014), Science and Technology Research Project of Department of Education of Heilongjiang Province (12521401), and Foundational Science Foundation of Harbin Engineering University and Fundamental Research Funds for the Central Universities (HEUCF20131101).

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

XU Run-Zhang, DING Yun-Hua

College of Science, Harbin Engineering University, Harbin 150001, China

Received:2011-03-21 Revised:2012-08-04 Online:2013-05-20 Published:2013-05-20
Supported by:
The first author is supported by the National Natural Science Foundation of China (11101102), Ph.D. Programs Foundation of Ministry of Education of China (20102304120022), the Support Plan for the Young College Academic Backbone of Heilongjiang Province (1252G020), the Natural Science Foundation of Heilongjiang Province (A201014), Science and Technology Research Project of Department of Education of Heilongjiang Province (12521401), and Foundational Science Foundation of Harbin Engineering University and Fundamental Research Funds for the Central Universities (HEUCF20131101).

摘要/Abstract

摘要：

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 de-rived. 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.

关键词: Klein-Gordon equation, strongly damped, global solutions, blow up

Abstract:

Key words: Klein-Gordon equation, strongly damped, global solutions, blow up

中图分类号:

35A01

徐润章, 丁云华. GLOBAL SOLUTIONS AND FINITE TIME BLOW UP FOR DAMPED KLEIN-GORDON EQUATION[J]. 数学物理学报(英文版), 2013, 33(3): 643-652.

XU Run-Zhang, DING Yun-Hua. GLOBAL SOLUTIONS AND FINITE TIME BLOW UP FOR DAMPED KLEIN-GORDON EQUATION[J]. Acta mathematica scientia,Series B, 2013, 33(3): 643-652.

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

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

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