ON A CLASS OF SINGULARLY PERTURBED ELLIPTIC SYSTEMS WITH ASYMPTOTIC PHASE SEGREGATION

Bozorgnia F, Burger M, Fotouhi M (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Discrete and Continuous Dynamical Systems American Institute of Mathematical Sciences (AIMS)

DOI: 10.3934/dcds.2022023

Abstract

This work is devoted to study a class of singular perturbed elliptic systems and their singular limit to a phase segregating system. We prove existence and uniqueness and study the asymptotic behavior of 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 that all components can not coexist simultaneously. We present a novel method, which provides an explicit solution of the limiting problem for a special choice of parameters. Moreover, we present some numerical simulations of the asymptotic problem.

Authors with CRIS profile

Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

University of Lisbon / Universidade de Lisboa (ULisboa) PT Portugal (PT) Sharif University of Technology / دانشگاه صنعتی شریف (SUT) IR Iran, Islamic Republic of (IR)

How to cite

APA:

Bozorgnia, F., Burger, M., & Fotouhi, M. (2022). ON A CLASS OF SINGULARLY PERTURBED ELLIPTIC SYSTEMS WITH ASYMPTOTIC PHASE SEGREGATION. Discrete and Continuous Dynamical Systems. https://dx.doi.org/10.3934/dcds.2022023

MLA:

Bozorgnia, Farid, Martin Burger, and Morteza Fotouhi. "ON A CLASS OF SINGULARLY PERTURBED ELLIPTIC SYSTEMS WITH ASYMPTOTIC PHASE SEGREGATION." Discrete and Continuous Dynamical Systems (2022).

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