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Nonexistence of global solutions of a nonlinear hyperbolic system |
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| Authors: | Keng Deng |
| Affiliation: | Department of Mathematics, University of Southwestern Louisiana, Lafayette, Louisiana 70504 |
| Abstract: | Consider the initial value problem
with |
| Keywords: | |
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![begin{equation*}begin {array}{llll} u_{tt} = Delta u+vert vvert ^{p}, & v_{tt} = Delta v +vert uvert ^{q}, &xin mathbb {R}^{n},&t>0, [2jot ] u(x,0)=f(x),&v(x,0)=h(x),&{}&{} [2jot ] u_{t}(x,0) = g(x), &v_{t}(x,0) = k(x), &{}&{} end {array} end{equation*}](http://www.ams.org/tran/1997-349-04/S0002-9947-97-01841-2/gif-abstract/img1.gif)
and 
. We show that there exists a bound 
such that if 
all nontrivial solutions with compact support blow up in finite time.