Degeneration of boundary layer at singular points

• Main Authors: Dyachenko, Evgueniya, Tarkhanov, Nikolai
• Format: Others
• Language: English
• Published: Universität Potsdam 2012
• Subjects: Heat equation; Dirichlet problem; characteristic points; boundary layer; Mathematics
• Online Access: http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60135; http://opus.kobv.de/ubp/volltexte/2012/6013/

We study the Dirichlet problem in a bounded plane domain for the heat equation with small parameter multiplying the derivative in t. The behaviour of solution at characteristic points of the boundary is of special interest. The behaviour is well understood if a characteristic line is tangent to the boundary with contact degree at least 2. We allow the boundary to not only have contact of degree less than 2 with a characteristic line but also a cuspidal singularity at a characteristic point. We construct an asymptotic solution of the problem near the characteristic point to describe how the boundary layer degenerates.