Acta mathematica scientia, Series B >
GLOBAL SOLUTIONS AND FINITE TIME BLOW UP FOR DAMPED KLEIN-GORDON EQUATION
Received date: 2011-03-21
Revised date: 2012-08-04
Online 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).
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.
Key words： Klein-Gordon equation; strongly damped; global solutions; blow up
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 . DOI: 10.1016/S0252-9602(13)60027-2
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