Dept. Math, Hokkaido Univ. EPrints Server

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

Preprint Series # 967
Takamura, Hiroyuki and Uesaka, Hiroshi and Wakasa, Kyouhei Sharp blow-up for semilinear wave equations with non-compactly supported data. (03 September 2010); (Submitted)

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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 finite propagation speed of the linear wave. Our theorem clarifies the final criterion on such a phenomenon.

Item Type:Preprint
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:2116