TY  - JOUR
A1  - Kiselev, Oleg M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The capture of a particle into resonance at potential hole with dissipative perturbation
JF  - Chaos, solitons & fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science
N2  - We study the capture of a particle into resonance at a potential hole with dissipative perturbation and external periodic excitation. The measure of resonance solutions is evaluated. We also derive an asymptotic formula for the parameter range of those solutions which are captured into resonance.
Y1  - 2014
U6  - https://doi.org/10.1016/j.chaos.2013.11.003
SN  - 0960-0779
SN  - 1873-2887
VL  - 58
SP  - 27
EP  - 39
PB  - Elsevier
CY  - Oxford
ER  - 
TY  - INPR
A1  - Kiselev, Oleg M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Scattering of autoresonance trajectories upon a separatrix
N2  - We study asymptotic properties of solutions to the primary resonance equation with large amplitude on a long time interval.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 2 
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56880
ER  - 
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
JF  - 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
U6  - https://doi.org/10.1007/s11253-015-1038-8
SN  - 0041-5995
SN  - 1573-9376
VL  - 66
IS  - 10
SP  - 1455
EP  - 1474
PB  - Springer
CY  - New York
ER  -