Dynamic Boundary Conditions with Memory: Well-Posedness and Attractors for Coleman-Gurtin Equations
In this joint work with Ciprian G. Gal (Florida International University), we report some recent advances concerning a Coleman-Gurtin equation with singularly perturbed memory relaxation, equipped with dynamic boundary conditions also possessing memory. Nonlinear terms are defined on the interior of the domain and on the boundary, subject to either classical dissipation assumptions with no growth assumption, or to a generalized balance condition. Additionally, we do not assume the interior and the boundary share the same memory response. Under stronger assumptions, we obtain a family of exponential attractors that is robust (Hölder continuous) with respect to the relaxation parameter.