Differential and Integral Equations

Global solutions to boundary value problems for a nonlinear wave equation in high space dimensions

Keith Agre and Mohammad A. Rammaha

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Abstract

In this article we consider an initial--boundary value problem for a wave equation in high dimensions with a nonlinear damping term that is not Lipschitz in $u_t$. We establish the existence and uniqueness of a global solution by using a compactness method and by exploiting the monotonicity property of the nonlinearity.

Article information

Source
Differential Integral Equations, Volume 14, Number 11 (2001), 1315-1331.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356123026

Mathematical Reviews number (MathSciNet)
MR1859608

Zentralblatt MATH identifier
1161.35438

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35A35: Theoretical approximation to solutions {For numerical analysis, see 65Mxx, 65Nxx} 35L20: Initial-boundary value problems for second-order hyperbolic equations

Citation

Agre, Keith; Rammaha, Mohammad A. Global solutions to boundary value problems for a nonlinear wave equation in high space dimensions. Differential Integral Equations 14 (2001), no. 11, 1315--1331. https://projecteuclid.org/euclid.die/1356123026


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