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1995 Blow-up for semilinear wave equations with slowly decaying data in high dimensions
Hiroyuki Takamura
Differential Integral Equations 8(3): 647-661 (1995). DOI: 10.57262/die/1369316512


We are concerned with classical solutions to the initial value problem for $\square u=|u|^p$ or $\square u=|u_t|^p$ in $\Bbb R^n\times[0,\infty)$ with \lq\lq small" data. If the data have compact support, it is partially known that there is a critical number $p_0(n)$ such that most solutions blow-up in finite time for $1<p\le p_0(n)$ and a global solution exists for $p>p_0(n)$. In this paper, we shall show for all $n\ge2$ that, if the support of data is noncompact, there are blowing-up solutions even for $p>p_0(n)$ because of the \lq\lq bad" spatial decay of the initial data. Moreover, critical decays for each equation are conjectured. The proof lies in the pointwise estimates of the fundamental solution of $\square$.


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Hiroyuki Takamura. "Blow-up for semilinear wave equations with slowly decaying data in high dimensions." Differential Integral Equations 8 (3) 647 - 661, 1995.


Published: 1995
First available in Project Euclid: 23 May 2013

zbMATH: 0848.35017
MathSciNet: MR1306581
Digital Object Identifier: 10.57262/die/1369316512

Primary: 35B05
Secondary: 35B40 , 35L70

Rights: Copyright © 1995 Khayyam Publishing, Inc.


Vol.8 • No. 3 • 1995
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