TY  - JOUR
A1  - Antoniouk, Alexandra Viktorivna
A1  - Kiselev, Oleg M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point
T2  - Ukrainian mathematical journal
N2  - The Dirichlet problem for the heat equation in a bounded domain aS, a"e (n+1) is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane t = c, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guaranteeing that the solution is continuous up to the characteristic point were established by Petrovskii (1934) under the assumption that the Dirichlet data are continuous. The appearance of Petrovskii's paper was stimulated by the existing interest to the investigation of general boundary-value problems for parabolic equations in bounded domains. We contribute to the study of this problem by finding a formal solution of the Dirichlet problem for the heat equation in a neighborhood of a cuspidal characteristic boundary point and analyzing its asymptotic behavior.
Y1  - 2015
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/39094
SN  - 0041-5995
SN  - 1573-9376
VL  - 66
IS  - 10
SP  - 1455
EP  - 1474
PB  - Springer
CY  - New York
ER  -