Degeneration of boundary layer at singular points

Dyachenko, Evgueniya; Tarkhanov, Nikolai Nikolaevich

Treffer 28 von 35

Degeneration of boundary layer at singular points

Evgueniya Dyachenko, Nikolai Nikolaevich Tarkhanov

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.

Metadaten
Verfasserangaben:	Evgueniya Dyachenko, Nikolai Nikolaevich Tarkhanov ORCiD GND
URN:	urn:nbn:de:kobv:517-opus-60135
Schriftenreihe (Bandnummer):	Preprints des Instituts für Mathematik der Universität Potsdam (1(2012)23)
Publikationstyp:	Preprint
Sprache:	Englisch
Erscheinungsjahr:	2012
Veröffentlichende Institution:	Universität Potsdam
Datum der Freischaltung:	06.07.2012
Freies Schlagwort / Tag:	Dirichlet problem; Heat equation; boundary layer; characteristic points
Organisationseinheiten:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC-Klassifikation:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Klassifikation:	35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Gxx General higher-order equations and systems / 35G15 Boundary value problems for linear higher-order equations
	35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K35 Initial-boundary value problems for higher-order parabolic equations
	58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J35 Heat and other parabolic equation methods
Sammlung(en):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
Lizenz (Deutsch):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz
Externe Anmerkung:	RVK-Klassifikation: SI 990

Degeneration of boundary layer at singular points

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