2024/02/05 by Anna Logioti, Barbara Niethammer, Logioti, Anna +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #35Q92 #35R35 #35R37 #35R70 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2402.03034
openalex publication_date 2024/02/05 · openalex created_date 2024/02/08 · openalex updated_date 2026/08/01
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. In previous papers, we have established well-posedness of this problem and derived conditions on the initial data that imply continuity of the free boundary as t→ 0. In this paper we extend the qualitative study of the free boundary by considering axisymmetric data. Under additional monotonicity assumptions on the data we prove global continuity of the free boundary. On the other hand, if the initial data violate a "no-fattening" condition we show that the free boundary can oscillate as t → 0.