Martedì 18 Settembre 2018, alle ore 15 precise, presso la sala conferenze dell’IMATI-CNR di Pavia, la
d.ssa Lara Trussandi, Universität Wien
terrà un seminario dal titolo:
From nonlocal to local Cahn-Hilliard equation
nell'ambito del Seminario di Matematica Applicata (IMATI-CNR e Dipartimento di Matematica, Pavia),
Al termine della conferenza sarà organizzato un piccolo rinfresco.
Abstract. The Cahn-Hilliard equation is widely used in the study of phase field models. A nonlocal version of the equation, proposed by Giacomin and Lebowitz, attracted great interest in recent years. In this talk I will present the convergence of a nonlocal version of the Cahn-Hilliard equation to its local counterpart as the nonlocal convolution kernel approximates a Dirac delta in a periodic boundary conditions setting. This convergence result strongly relies on the dynamics of the problem. More precisely, the H-1 -gradient flow structure of the equation allows to deduce uniform H1 estimates for solutions of the nonlocal Cahn-Hilliard equation and, together with a Poincaré type inequality by Ponce, provides the compactness argument that allows to prove the convergence result.