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

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.