Analysis of hysteretic reaction-diffusion systems

Chiu, Chichia; Walkington, Noel

doi:10.1090/qam/1604805

Authors: Chichia Chiu and Noel Walkington
Journal: Quart. Appl. Math. 56 (1998), 89-106
MSC: Primary 92D25; Secondary 35K57, 47D06, 47N20
DOI: https://doi.org/10.1090/qam/1604805
MathSciNet review: MR1604805
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Abstract: In this paper, we consider a mathematical model motivated by patterned growth of bacteria. The model is a system of differential equations that consists of two sub-systems. One is a system of ordinary differential equations and the other one is a reaction-diffusion system. Pattern formation in this model is caused by an initial instability of the ordinary differential equations. However, nonlinear coupling to the reaction-diffusion system stabilizes the ordinary differential equations resulting in stationary long-time behavior. We establish existence, uniqueness, and characterize long-time behavior of the solutions.

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