Bulk-surface systems on evolving domains

2022/12/26 by Diogo Caetano, Charles M. Elliott, Caetano, Diogo +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Caveolin-1 and cellular processes #FOS: Mathematics #Mathematical Biology Tumor Growth

paper · doi:10.48550/arxiv.2212.13288

openalex publication_date 2022/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions. This is achieved by proving L^p-maximal regularity of parabolic equations and duality methods in moving surfaces, which are of independent interest. The second main result is the large time dynamics where we show, under the assumption that the volume/area of the moving domain/surface is unchanged and that the material velocities are decaying for large time, that the solution converges to a unique spatially homogeneous equilibrium. The result is proved by extending the entropy method to bulk-surface systems in evolving domains.

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