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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Nonexistence of global solutions of
a nonlinear hyperbolic system

Author: Keng Deng
Journal: Trans. Amer. Math. Soc. 349 (1997), 1685-1696
MSC (1991): Primary 35L15, 35L55, 35L70
MathSciNet review: 1401767
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Abstract | References | Similar Articles | Additional Information

Abstract: Consider the initial value problem

\begin{equation*}\begin {array}{llll} u_{tt} = \Delta u+\vert v\vert ^{p}, & v_{tt} = \Delta v +\vert u\vert ^{q}, &x\in \mathbb {R}^{n},&t>0, \\ [2\jot ] u(x,0)=f(x),&v(x,0)=h(x),&{}&{} \\ [2\jot ] u_{t}(x,0) = g(x), &v_{t}(x,0) = k(x), &{}&{} \end {array} \end{equation*}

with $1\le n\le 3$ and $p,q>0$. We show that there exists a bound $B(n)\ (\le \infty )$ such that if $1<pq<B(n)$ all nontrivial solutions with compact support blow up in finite time.

References [Enhancements On Off] (What's this?)

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Additional Information

Keng Deng
Affiliation: Department of Mathematics, University of Southwestern Louisiana, Lafayette, Louisiana 70504

Received by editor(s): March 16, 1995
Received by editor(s) in revised form: December 1, 1995
Article copyright: © Copyright 1997 American Mathematical Society

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