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| We report some recent advances concerning the well-posedness of the Coleman-Gurtin equation equipped with dynamic boundary conditions that also possess memory relaxation. Weak solutions are obtained from a Galerkin procedure whereby nonlinear terms with arbitrary polynomial growth are defined on the interior of the domain and on the boundary, subject to either classical dissipation assumptions, or to a generalized balance condition. In general, we do not assume the interior and the boundary share the same memory response. Under additional assumptions, we arrive at a formulation for strong solutions, and a hybrid-solution situated between the strong and weak formulations. |
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