Calculus of Variations and Geometric Measure Theory
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A. Bach - T. Esposito - R. Marziani - C. I. Zeppieri

Interaction between oscillations and singular perturbations in a one-dimensional phase-field model

created by bach on 14 Jun 2021
modified by zeppieri1 on 08 Jan 2022

[BibTeX]

Accepted Paper

Inserted: 14 jun 2021
Last Updated: 8 jan 2022

Journal: AWM Volume - Research in the Mathematics of Materials Science
Year: 2022

Abstract:

In this note we study the relative impact of fine-scale heterogeneities and singular perturbations in a one-dimensional phase-field model of Ambrosio-Tortorelli type. We show that the limit functional is always of Mumford-Shah type, with a surface term depending on the mutual converging rate of the oscillation and the perturbation parameter.

Keywords: $\Gamma$-convergence, singular perturbations, homogenisation


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