Open AccessOn a class of singularly perturbed elliptic systems with asymptotic phase segregation
Author(s) -
Farid Bozorgnia,
Martin Burger
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.