Abstract
In this article, we continue the analysis of a class of singularly perturbed parabolic equations with alternating boundary layer type solutions. For such problems, the degenerate (reduced) equations obtained by setting a small parameter equal to zero correspond to algebraic equations that have several isolated roots. As time increases, solutions of these equations periodically go through two comparatively long lasting stages with fast transitions between these stages. During one of these stages, the solution outside the boundary layer (i.e. The regular part of the asymptotic solution) is close to one of the roots of the degenerate equation. During the other stage, the regular part of the asymptotic solution is close to the other root. Here we discuss some specific features of the solutions' behavior for such problems in certain two-dimensional spatial domains.
| Original language | English |
|---|---|
| Article number | 1350029 |
| Journal | Analysis and Applications |
| Volume | 11 |
| Issue number | 5 |
| DOIs | |
| State | Published - Sep 2013 |
Funding
This work was supported in part by the faculty exchange grant from The University of Montana awarded to Leonid Kalachev. The authors would like to thank two anonymous reviewers for a number of helpful comments which led to substantial improvement of the manuscript.
Keywords
- Boundary function method
- Parabolic equations
- Singular perturbations
- Two-dimensional spatial domains