The University of Montana
Department of Mathematical Sciences

Technical report #1/2004

Singularly Perturbed Parabolic Equations with Alternating Boundary Layer Type Solutions

Adelaida B. Vasil'eva
Department of Physics, Moscow State University, Moscow, 119899 Russia
E-mail: abvas@mathabv.phys.msu.su

and

Leonid V. Kalachev
Department of Mathematical Sciences, University of Montana, Missoula, MT 59812, USA
E-mail: kalachev@mso.umt.edu

Abstract

We consider singularly perturbed parabolic equations for which the degenerate equations obtained by setting small parameter to zero are the algebraic equations that have several roots. We study boundary layer type solutions that, as time increases, periodically go through two fairly long lasting stages with extremely fast transitions between these two stages. During one of these stages the solution outside the boundary layer is close to one of the roots of the degenerate (reduced) equation, while during the other stage the solution is close to the other root.

Keywords: singular perturbations, parabolic equations, boundary function method

AMS Subject Classification: 34E10, 35B05, 35B25

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