TY  - JOUR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolaj Nikolaevič
T1  - Asymptotic expansions at nonsymmetric cuspidal points
JF  - Mathematical notes
N2  - We study the asymptotics of solutions to the Dirichlet problem in a domain X subset of R3 whose boundary contains a singular point O. In a small neighborhood of this point, the domain has the form {z > root x(2) + y(4)}, i.e., the origin is a nonsymmetric conical point at the boundary. So far, the behavior of solutions to elliptic boundary-value problems has not been studied sufficiently in the case of nonsymmetric singular points. This problem was posed by V.A. Kondrat'ev in 2000. We establish a complete asymptotic expansion of solutions near the singular point.
KW  - Dirichlet problem
KW  - singular points
KW  - asymptotic expansions
Y1  - 2020
U6  - https://doi.org/10.1134/S0001434620070238
SN  - 0001-4346
SN  - 1573-8876
VL  - 108
IS  - 1-2
SP  - 219
EP  - 228
PB  - Springer Science
CY  - New York
ER  - 
TY  - INPR
A1  - Dyachenko, Evgueniya
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Degeneration of boundary layer at singular points
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)23 
KW  - Heat equation
KW  - Dirichlet problem
KW  - characteristic points
KW  - boundary layer
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60135
ER  -