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| In this talk, we consider the initial value problem for semilinear wave equations with non-compactly supported data. With the initial data of zero initial position, the solution blows up for any power nonlinearity. This was first shown by Asakura (1986) under the assumption that the spatial decay is weak at infinity. On the other hand, Takamura & Uesaka & Wakasa (2010) have obtained the blow up result for non-zero initial position by making use of "time-derivative reduction".
Our aim in this talk is to show the blow up result when both the initial position and the initial velocity do not identically vanish. |
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