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 fi determines the weighted surface measure dS=β on the boundary of the given spatial domain, in the appropriate Hilbert space that makes the generator for the problem self-adjoint. Usually, β is continuous and bounded away from both zero and infinity, and thus L2 (∂Ω,dS) and L2 (∂Ω,dS=β) are equal as sets. In this paper this restriction is eliminated, so that both zero and infinity are allowed to be limiting values for β. An application includes the parabolic asymptotics for the Wentzell telegraph equation and strongly damped Wentzell wave equation with general β.
Discrete and Continuous Dynamical Systems - Series S
Clendenen, R., Goldstein, G., & Goldstein, J. (2016). Degenerate flux for dynamic boundary conditions in parabolic and hyperbolic equations. Discrete and Continuous Dynamical Systems - Series S, 9 (3), 651-660. https://doi.org/10.3934/dcdss.2016019