Reaction-diffusion models with a conservation law and pattern formations

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  • Modeling and Simulation in Applied Mathematics : Proceedings of Annual Workshop on Modeling and Simulation in Applied Mathematics, December 20, 2015 JOSAI UNIVERSITY

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A two-component reaction-diffusion system with a mass conservation property is given as a model of the cell polarity. We first review mathematical aspects of the model system. Then based on it, we provide an extended system of three components with the mass conservation, which is regarded as a perturbed system of the two component one when the coupling parameter is small. We show that the system possesses a unique positive constant steady state under a certain condition on the total mass. Then numerical simulations subject to the periodic boundary condition exhibit coexistence of two stable solutions that are the constant steady state and a single spike solution. Moreover, in the transient dynamics Turing-like patterns emerge, though no diffusion driven instability for the constant steady state takes place.

Modeling and Simulation in Applied Mathematics : Proceedings of Annual Workshop on Modeling and Simulation in Applied Mathematics, held at Josai Unversity on December 20 in 2015 / edited by Masahiro FUJITA, Manabu INUMA, Takahiro TSUCHIYA, Hidenori YASUDA

identifier:JOS-13447777-0913

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