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The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary (2212.11241v1)
Published 21 Dec 2022 in math.AP
Abstract: We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the layer tends to zero. We also discuss $\Gamma$-convergence of the functionals generating these flows. Our analysis of strong solutions depends on a new version of the Reilly identity.