Thursday, 3 October 2019, 2.15 p.m. (sharp),

Luca Scarpa, University of Vienna

at the conference room of IMATI CNR in Pavia, will give a lecture titled:

Nonlocal-to-local asymptotics of viscous Cahn-Hilliard equations with Neumann boundary conditions

At the end a refreshment will be organized.

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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).