Differential and Integral Equations

Systems of nonlinear wave equations with damping and source terms

Keith Agre and M. A. Rammaha

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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.

Article information

Source
Differential Integral Equations, Volume 19, Number 11 (2006), 1235-1270.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050301

Mathematical Reviews number (MathSciNet)
MR2278006

Zentralblatt MATH identifier
1212.35268

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35L20: Initial-boundary value problems for second-order hyperbolic equations

Citation

Agre, Keith; Rammaha, M. A. Systems of nonlinear wave equations with damping and source terms. Differential Integral Equations 19 (2006), no. 11, 1235--1270. https://projecteuclid.org/euclid.die/1356050301


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