Publication 20-CNA-001

Sharp Interface Limit Of A Multi-Phase Transitions Model Under Nonisothermal Conditions

Riccardo Cristoferi
Department of Mathematical Sciences
Heriot-Watt University
Edinburgh EH14 4AS, United Kingdom
r.cristoferi@hw.ac.uk

Giovanni Gravina
Department of Mathematical Analysis
Faculty of Mathematics and Physics, Charles University
Prague, Czech Republic
gravina@karlin.mff.cuni.cz

Abstract: A vectorial Modica-Mortola functional is considered and the convergence to a sharp interface model is studied. The novelty of the paper is that the wells of the potential are not constant, but depend on the spatial position in the domain $\Omega$. The mass constrained minimization problem and the case of Dirichlet boundary conditions are also treated. The proofs rely on the precise understanding of minimizing geodesics for the degenerate metric induced by the potential.

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