Degeneration of Boundary Layer at Singular Points

Evgueniya Dyachenko ; Nikolai Tarkhanov

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 3, pp. 283-297.

Résumé

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.

Détail

Keywords: Heat equation, Dirichlet problem, characteristic points, boundary layer.

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