# American Institute of Mathematical Sciences

2011, 2011(Special): 1351-1357. doi: 10.3934/proc.2011.2011.1351

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

 1 Department of Complex and Intelligent Systems, Faculty of Systems Information Science, Future University Hakodate, 116-2 Kamedanakano-cho, Hakodate, Hokkaido 041-8655, Japan 2 Department of Mathematics, College of Science and Technology, Nihon University, Chiyodaku Kanda Surugadai 1-8, Tokyo, 101-8308, Japan 3 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

Received  July 2010 Revised  August 2010 Published  October 2011

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.
Citation: Hiroyuki Takamura, Hiroshi Uesaka, Kyouhei Wakasa. Sharp blow-up for semilinear wave equations with non-compactly supported data. Conference Publications, 2011, 2011 (Special) : 1351-1357. doi: 10.3934/proc.2011.2011.1351
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