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2003 Bifurcating positive stable steady-states for a system of damped wave equations
Anthony W. Leung
Differential Integral Equations 16(4): 453-471 (2003).

Abstract

A system of nonlinear damped wave equations with symmetric linear part is investigated. A positive steady-state bifurcates from the trivial solution as a parameter changes. The spectrum of the linearized operator is studied. Then the stability of the positive steady-state is considered as a solution of the nonlinear hyperbolic system. Asymptotic stability results are found for solutions in $R^{N},$ $ N \ge 1.$ Bifurcation methods are used to find the steady-states, and semigroup methods are used to study stability. Stability results are obtained although the semigroup is not analytic.

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Anthony W. Leung. "Bifurcating positive stable steady-states for a system of damped wave equations." Differential Integral Equations 16 (4) 453 - 471, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1041.35046
MathSciNet: MR1972875

Subjects:
Primary: 35L70
Secondary: 35B32 , 35B40 , 47J15

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 4 • 2003
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