On a class of singularly perturbed elliptic systems with asymptotic phase segregation | Zendy

Farid Bozorgnia | Zendy; Martin Burger | Zendy; Morteza Fotouhi | Zendy

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On a class of singularly perturbed elliptic systems with asymptotic phase segregation

Author(s) -

Farid Bozorgnia,

Martin Burger,

Morteza Fotouhi

Publication year - 2022

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2022023

Subject(s) - uniqueness , limiting , limit (mathematics) , class (philosophy) , mathematics , infinity , asymptotic analysis , singular perturbation , domain (mathematical analysis) , boundary (topology) , mathematical analysis , singular point of a curve , method of matched asymptotic expansions , work (physics) , boundary value problem , homogeneous , point (geometry) , phase (matter) , computer science , combinatorics , physics , geometry , mechanical engineering , quantum mechanics , artificial intelligence , engineering , thermodynamics

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.

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