Asymptotically Stable Invariant Manifold for Coupled Nonlinear Parabolic-Hyperbolic Partial Differential Equations
by
Anthony W. Leung
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221

The article considers a coupled system of nonlinear parabolic and hyperbolic partial differential equations which arises in the study of wave phenomena which are heat generating or temperature related. Under appropriate conditions, for example high thermal diffusivity, it is proved that there exists an invariant manifold for the full system of equations. The asymptotic stability of the invariant manifold is also considered. Moreover, it is shown that an equilibrium which is asymptotically stable for flows on the invariant manifold will be asympotically stable for the full system. The method can further be modified for application to fluid and magnetic interactions.

Date received: December 12, 2002