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2006 Systems of nonlinear wave equations with damping and source terms
Keith Agre, M. A. Rammaha
Differential Integral Equations 19(11): 1235-1270 (2006).

Abstract

In this article we focus on the global well posedness of the system of nonlinear wave equations \begin{align*} u_{tt}- \Delta u + |u_{t}|^{m-1} u_{t}= f_{1}(u,v)\\ v_{tt}- \Delta v + |v_{t}|^{r-1} v_{t}= f_{2}(u,v) \end{align*} in a bounded domain $\Omega\subset\mathbb{R}^{n}$, $n = 1,2,3,$ with Dirichlét boundary conditions. Under some restriction on the parameters in the system we obtain several results on the existence of local and global solutions, uniqueness, and the blow up of solutions in finite time.

Citation

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Keith Agre. M. A. Rammaha. "Systems of nonlinear wave equations with damping and source terms." Differential Integral Equations 19 (11) 1235 - 1270, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35268
MathSciNet: MR2278006

Subjects:
Primary: 35L70
Secondary: 35B30, 35L20

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 11 • 2006
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