Differential and Integral Equations

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

Anthony W. Leung

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

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: 35B32: Bifurcation [See also 37Gxx, 37K50] 35B40: Asymptotic behavior of solutions 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]


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

Export citation