DEGENERATE FLUX FOR DYNAMIC BOUNDARY CONDITIONS IN PARABOLIC AND HYPERBOLIC EQUATIONS

In the dynamic or Wentzell boundary condition for elliptic, parabolic and hyperbolic partial differential equations, the positive flux coefficient beta determines the weighted surface measure dS/beta on the boundary of the given spatial domain, in the appropriate Hilbert space that makes the generator for the problem selfadjoint. Usually, beta is continuous and bounded away from both zero and infinity, and thus L-2 (partial derivative Omega, dS) and L-2 (partial derivative Omega, dS/beta) are equal as sets. In this paper this restriction is eliminated, so that both zero and infinity are allowed to be limiting values for beta. An application includes the parabolic asymptotics for the Wentzell telegraph equation and strongly damped Wentzell wave equation with general beta.