Asymptotic analysis of phase-field models

25 February 2021
Andreas Muench

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We study the evolution of solid surfaces and pattern formation by
surface diffusion. Phase field models with degenerate mobilities are
frequently used to model such phenomena, and are validated by
investigating their sharp interface limits. We demonstrate by a careful
asymptotic analysis involving the matching of exponential terms that a
certain combination of degenerate mobility and a double well potential
leads to a combination of both surface and non-linear bulk diffusion to
leading order. If time permits, we will discuss implications and extensions.

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  • Industrial and Applied Mathematics Seminar