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math.AP2022
The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary
Yoshikazu Giga, Michał Łasica, Piotr Rybka
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 la…
math.AP2022
Convergence of solutions to a convective Cahn-Hilliard type equation of the sixth order in case of small deposition rates
Piotr Rybka, Glen Wheeler
We show stabilisation of solutions to the sixth-order convective Cahn-Hilliard equation. {The problem} has the structure of a gradient flow perturbed by a quadratic destabilising t…