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

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.

References in corpus (2)

• Nonlocal-to-local convergence of Cahn-Hilliard equations: Neumann boundary conditions and viscosity terms
• Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics

Cited by in corpus (2)

• On the nonlocal Cahn--Hilliard equation with nonlocal dynamic boundary condition and boundary penalization
• On a nonlocal Cahn-Hilliard model permitting sharp interfaces