Transactions of the American Mathematical Society

Author(s): Keng Deng
Journal: Trans. Amer. Math. Soc. 349 (1997), 1685-1696.
MSC (1991): Primary 35L15, 35L55, 35L70
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$\begin{equation*}\begin {array}{llll} u_{tt} = \Delta u+\vert v\vert ^{p}, & v_{tt} = \Delta v +\vert u\vert ^{q}, &x\in \mathbb {R}^{n},&t>0, [2\jot ] u(x,0)=f(x),&v(x,0)=h(x),&{}&{} [2\jot ] u_{t}(x,0) = g(x), &v_{t}(x,0) = k(x), &{}&{} \end {array} \end{equation*}$

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.

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