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arXiv · 1902.04469

Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics

Elisa Davoli·Helene Ranetbauer·Luca Scarpa·Lara Trussardi
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Abstract

Existence and uniqueness of solutions for nonlocal Cahn-Hilliard equations with degenerate potential is shown. The nonlocality is described by means of a symmetric singular kernel not falling within the framework of any previous existence theory. A convection term is also taken into account. Building upon this novel existence result, we prove convergence of solutions for this class of nonlocal Cahn-Hilliard equations to their local counterparts, as the nonlocal convolution kernels approximate a Dirac delta. Eventually, we show that, under suitable assumptions on the data, the solutions to the nonlocal Cahn-Hilliard equations exhibit further regularity, and the nonlocal-to-local convergence is verified in a stronger topology.

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Elisa Davoli, Helene Ranetbauer, Luca Scarpa, Lara Trussardi. 2019-02-12. Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics. https://doi.org/10.1016/j.anihpc.2019.10.002

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