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arXiv · 1911.12770

Local asymptotics for nonlocal convective Cahn-Hilliard equations with W^{1,1} kernel and singular potential

Elisa Davoli·Luca Scarpa·Lara Trussardi
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Abstract

We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in the case of a W^{1,1} convolution kernel and under homogeneous Neumann conditions. Any type of potential, possibly also of double-obstacle or logarithmic type, is included. Additionally, we highlight variants and extensions to the setting of periodic boundary conditions and viscosity contributions, as well as connections with the general theory of evolutionary convergence of gradient flows.

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Elisa Davoli, Luca Scarpa, Lara Trussardi. 2019-11-28. Local asymptotics for nonlocal convective Cahn-Hilliard equations with W^{1,1} kernel and singular potential. https://doi.org/10.1016/j.jde.2021.04.016

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