Differential and Integral Equations

Systems of nonlinear wave equations with damping and source terms

Keith Agre and M. A. Rammaha

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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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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