From nonlocal to local Cahn-Hilliard equation
Dr. Lara Trussardi, Universität Wien
Sala conferenze IMATI-CNR, Pavia - Tuesday, September 18, 2018 h.15:00
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.
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