Single Transition Layer in Mass-Conserving Reaction-Diffusion Systems with Bistable Nonlinearity

Autor:	Kuwamura, Masataka, Teramoto, Takashi, Ikeda, Hideo
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs 35B25 35K57
Druh dokumentu:	Working Paper
Popis:	Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of stationary solutions with a single internal transition layer in such reaction-diffusion systems under general assumptions by the singular perturbation theory. Moreover, we present a meaningful model for understanding the existence of an unstable transition layer solution; our numerical simulations show that the unstable solution is a separatrix of the dynamics of the model. Comment: 41 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.00227 Zobrazit plný text záznamu View this record from Arxiv