Differential and Integral Equations

Bifurcating positive stable steady-states for a system of damped wave equations

Anthony W. Leung

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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.

Article information

Source
Differential Integral Equations, Volume 16, Number 4 (2003), 453-471.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060653

Mathematical Reviews number (MathSciNet)
MR1972875

Zentralblatt MATH identifier
1041.35046

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B32: Bifurcation [See also 37Gxx, 37K50] 35B40: Asymptotic behavior of solutions 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]

Citation

Leung, Anthony W. Bifurcating positive stable steady-states for a system of damped wave equations. Differential Integral Equations 16 (2003), no. 4, 453--471. https://projecteuclid.org/euclid.die/1356060653


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