## Differential and Integral Equations

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

### Systems of nonlinear wave equations with damping and source terms

#### 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