Special properties of the stationary solution for two‐dimensional singularly perturbed parabolic problem, stability, and attraction domain

Abstract

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.