Nonlocal-to-local asymptotics of viscous Cahn-Hilliard equations with Neumann boundary conditions
Luca Scarpa, University of Vienna
Sala conferenze IMATI-CNR, Pavia – Giovedì 3 Ottobre 2019 h.14:15
Abstract. We consider a class of nonlocal viscous Cahn-Hilliard equations with Neumann boundary conditions for the chemical potential. The double-well potential may be singular (e. g. of logarithmic type), and the convolution kernel is symmetric with a singularity of order 2 in the origin. First of all, we show that the nonlocal problem
is well posed in a suitable variational sense. Secondly, we prove that the nonlocal solutions converge to the corresponding ones of the local system with Neumann boundary conditions for the concentration and the chemical potential, as the convolution kernel approaches a Dirac delta. The asymptotic behaviour is analyzed by means of Gamma convergence results, both when the limiting local Cahn-Hilliard equation is of viscous type and of pure type. This study is based a joint work with Elisa Davoli and Lara Trussardi (University of Vienna, Austria).