Traveling Phase Interfaces in Viscous Forward–Backward Diffusion Equations

MCML Authors

Carina Geldhauser

Dr.

* Former Member

→ Group Massimo Fornasier
 Applied Numerical Analysis

Abstract

The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical understanding of the intricate multiscale evolution is still missing. We shed light on the fine structure of propagating phase boundaries by carefully examining traveling wave solutions in a special case. Assuming a trilinear constitutive relation we characterize all waves that possess a monotone profile and connect the two phases by a single interface of positive width. We further study the two sharp-interface regimes related to either vanishing viscosity or the bilinear limit.

article

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Journal of Dynamics and Differential Equations

Aug. 2024.

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Authors

C. Geldhauser • M. Herrmann • D. Janßen

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Links

DOI

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Research Area

 A2 | Mathematical Foundations