On a stochastic phase-field model of cell motility with singular diffusion

2026/01/31 by Amjad Saef, Wilhelm Stannat
Mathematics · #math.PR #math.AP #msc:35K55 #msc:60H15 #msc:80A22 #msc:92C17 #msc:92D25

paper · pdf

published as Nonlinear Analysis, Vol. 274, January 2027, 114238 · 39 pages

arxiv created 2026/06/11 · arxiv updated 2026/08/06

Abstract

We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a phase-field. We investigate both the case of an independently evolving phase-field and of coupled phase-field evolution driven by a viscous Hamilton-Jacobi equation. Such systems are used in the modelling of single-cell chemotaxis, where the contour of the cell shape corresponds to a level set of the phase-field. The technical challenge lies in the singularities at zero level sets of the phase-field. For large classes of initial data, we establish global existence of probabilistically weak solutions in L²-spaces with weights which compensate for the singularities.

Citations

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