TY  - JOUR
A1  - Mera, Azal
A1  - Stepanenko, Vitaly A.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Successive approximation for the inhomogeneous burgers equation
JF  - Journal of Siberian Federal University : Mathematics & Physics
N2  - The inhomogeneous Burgers equation is a simple form of the Navier-Stokes equations. From the analytical point of view, the inhomogeneous form is poorly studied, the complete analytical solution depending closely on the form of the nonhomogeneous term.
KW  - Navier-Stokes equations
KW  - classical solution
Y1  - 2018
U6  - https://doi.org/10.17516/1997-1397-2018-11-4-519-531
SN  - 1997-1397
SN  - 2313-6022
VL  - 11
IS  - 4
SP  - 519
EP  - 531
PB  - Siberian Federal University
CY  - Krasnoyarsk
ER  - 
TY  - INPR
A1  - Antoniouk, Alexandra Viktorivna
A1  - Kiselev, Oleg
A1  - Stepanenko, Vitaly
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point
N2  - The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)25 
KW  - Heat equation
KW  - the first boundary value problem
KW  - characteristic boundary point
KW  - cusp
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-61987
ER  -