References & Citations
Mathematics > Analysis of PDEs
Title: Hysteretic dynamics of phase interfaces in bilinear forward-backward diffusion equations
(Submitted on 21 Apr 2024)
Abstract: We study single-interface solutions to a free boundary problem that couples bilinear bulk diffusion to the Stefan condition and a hysteretic flow rule for phase boundaries. We introduce a time-discrete approximation scheme and establish its convergence in the limit of vanishing step size. The main difficulty in our proof are strong microscopic oscillations which are produced by a propagating phase interface and need to be controlled on the macroscopic scale. We also present numerical simulations and discuss the link to the viscous regularization of ill-posed diffusion equations.
Submission history
From: Michael Herrmann [view email][v1] Sun, 21 Apr 2024 09:18:56 GMT (2087kb,D)
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