Asymptotic Stability, Local Uniqueness, and Domain of Attraction of Two-Dimensional Step Type Contrast Structures

I. V. Nedelko

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We prove the asymptotic stability of a two-dimensional stationary solution with internal transition layer to a singularly perturbed parabolic problem. We also construct a set of functions belonging to the domain of attraction of such a solution.

UDC: 517.956.226

Received: 21.12.1998

DOI: 10.4213/mzm485

 English version: Mathematical Notes, 2001, 69:1, 72–80

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