Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 53, Issue 1, Pages 1214-1238Publisher
SIAM PUBLICATIONS
DOI: 10.1137/20M1349114
Keywords
PDEs on surfaces; obstacle-type problem; stability of steady states
Categories
Funding
- Hausdorff Center of Mathematics at the University of Bonn
Ask authors/readers for more resources
This research examines a simple model for the response of biological cells to time-dependent signals and shows that the system converges to a bulk-surface parabolic obstacle problem in a suitable asymptotic limit. Furthermore, the study demonstrates an L-1 contraction property for this model and proves the stability of stationary states in the case of time-constant signals.
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 L-1-contraction property and, in the case of time-constant signals, the stability of stationary states.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available