2020/06/29 by Anna Logioti, Barbara Niethammer, Logioti, Anna +5
Mathematics · #35K86 #35R01 #35R35 #92C37 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35K86 #msc:35R01 #msc:35R35 #msc:92C37
paper · pdf · doi:10.48550/arxiv.2006.16155
26 pages
arxiv created 2020/06/29 · arxiv updated 2020/06/30
The amplification of an external signal is a key step in direction sensing of biological cells. We consider a simple model for the response to a time-depending signal, which was previously proposed by the last three authors. The model consists of a bulk-surface reaction-diffusion model. We prove that in a suitable asymptotic limit the system converges to a bulk-surface parabolic obstacle type problem. For this model and a reduction to a nonlocal surface equation we show an L1-contraction property and, in the case of time-constant signals, the stability of stationary states.