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Special properties of the stationary solution for two‐dimensional singularly perturbed parabolic problem, stability, and attraction domain
Author(s) -
Beloshapko Vera
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5235
Subject(s) - mathematics , degenerate energy levels , domain (mathematical analysis) , mathematical analysis , stationary solution , dirichlet problem , attraction , dirichlet boundary condition , boundary (topology) , weak solution , asymptotic expansion , stability (learning theory) , boundary problem , method of matched asymptotic expansions , boundary value problem , physics , linguistics , philosophy , machine learning , computer science , quantum mechanics
We consider a singularly perturbed elliptic Dirichlet problem in the case of a degenerate equation's multiple root. The existence of problem solution is proved. A complete asymptotic expansion of the solution is constructed and justified. It has distinctive features. The boundary layer becomes a three‐zone layer with different solution behavior in each of three zones. The solution of elliptic problem considered is a stationary solution of the corresponding parabolic problem. Asymptotic stability of this solution is proved and its attraction domain is found. We have considered the extended version of concept of stationary solution attraction domain.