Existence and stability of nonconstant positive steady states of morphogenesis models
Analysis of PDEs
2016-01-20 v1
Abstract
In this paper, We study an one--dimensional morphogenesis model considered by C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady states through local bifurcation theories. We also rigorously study the stability of the nonconstant solutions when the sensitivity function are chosen to be linear and logarithmic function respectively. Finally, we present numerical solutions to illustrate the formation of stable spatially inhomogeneous patterns. Our numerical simulations suggests that this model can develop very complicated and interesting structures even over one--dimensional finite domains.
Keywords
Cite
@article{arxiv.1407.1436,
title = {Existence and stability of nonconstant positive steady states of morphogenesis models},
author = {Haohao Chen and Bo Tong and Qi Wang},
journal= {arXiv preprint arXiv:1407.1436},
year = {2016}
}