Sharp-interface limit for non-isothermal and nonlocal Modica-Mortola functionals

Abstract

In this talk, we analyze a non-isothermal and nonlocal variant of the Modica-Mortola diffuse model for phase transitions. Here the classical gradient penalization is replaced by a nonlocal singular perturbation and the double-well potential is space-dependent. Our main result is the identification of the sharp-interface limit as the width of the transition layers converges to zero. This is joint work with Emanuele Tasso.