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arXiv · 1901.08750

On a Class of Singularly Perturbed Elliptic Systems with Asymptotic Phase Segregation

Farid Bozorgnia·Martin Burger
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Abstract

This work is devoted to study of a class of elliptic singular perturbed systems and their singular limit to a phase segregating system. We prove existence and uniqueness and study the asymptotic behaviour with convergence to a limiting problem as the interaction rate tends to infinity. The limiting problem is a free boundary problem such that at each point in the domain at least one of the components is zero which implies simultaneously all components can not coexist. We present a novel method, which provides an explicit solution of limiting problem for special choice of parameters. Moreover, we present some numerical simulations of the asymptotic problem.

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Farid Bozorgnia, Martin Burger. 2019-01-25. On a Class of Singularly Perturbed Elliptic Systems with Asymptotic Phase Segregation. https://arxiv.org/abs/1901.08750

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