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Sharp blow-up for semilinear wave equations with non-compactly supported data

Pages: 1351 - 1357, Issue Special, September 2011

 Abstract        Full Text (318.3K)              

Hiroyuki Takamura - Department of Complex and Intelligent Systems, Faculty of Systems Information Science, Future University Hakodate, 116-2 Kamedanakano-cho, Hakodate, Hokkaido 041-8655, Japan (email)
Hiroshi Uesaka - Department of Mathematics, College of Science and Technology, Nihon University, Chiyodaku Kanda Surugadai 1-8, Tokyo, 101-8308, Japan (email)
Kyouhei Wakasa - The 4th year of undergraduate, Department of Complex Systems, School of Systems Information Science, Future University Hakodate, 116-2 Kamedanakano-cho, Hakodate, Hokkaido 041-8655, Japan (email)

Abstract: This paper corrects Asakura's observation on semilinear wave equations with non-compactly supported data by showing a sharp blow-up theorem for classical solutions. We know that there is no global in time solution for any power nonlinearity if the spatial decay of the initial data is weak, in spite of nite propagation speed of the linear wave. Our theorem clari es the final criterion on such a phenomenon.

Keywords:  blow-up, semilinear wave equations
Mathematics Subject Classification:  Primary: 35L70; Secondary: 35B05, 35E15

Received: July 2010;      Revised: August 2010;      Published: October 2011.