Coleman-Gurtin type equations with dynamic boundary conditions

Abstract

We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory which includes the usual heat equation subject to a dynamic boundary condition as a special case. We investigate the well-posedness of systems which consist of Coleman-Gurtin type equations subject to dynamic boundary conditions, also with memory. Nonlinear terms are defined on the interior of the domain and on the boundary and subject to either classical dissipation assumptions, or to a nonlinear balance condition in the sense of [11]. Additionally, we do not assume that the interior and the boundary share the same memory kernel.

arXiv comment27 pages; to appear in Physica D: Nonlinear Phenomena

References in corpus (2)

• A New Approach to Equations with Memory
• Sharp estimates for the global attractor of scalar reaction-diffusion equations with a Wentzell boundary condition

Cited by in corpus (4)

• On $p$-Laplacian reaction-diffusion problems with dynamical boundary conditions in perforated media
• Robust Exponential Attractors for Coleman--Gurtin Equations with Dynamic Boundary Conditions Possessing Memory
• Global existence of weak solutions for strongly damped wave equations with nonlinear boundary conditions and balanced potentials
• Homogenization of parabolic problems with dynamical boundary conditions of reactive-diffusive type in perforated media