Abstract:
This work is devoted to an investigation of the asymptotic expansion for α→0 of Green's function Γ(x,t;x0) for the first boundary value problem for the equation Γt(x,t;x0)=α2Γxx(x,t;x0) for the case of a moving boundary. The asymptotic expansion is obtained by means of a modification of the method of heat potentials.
Bibliography: 5 titles.
Citation:
G. A. Nesenenko, “On the asymptotic expansion of Green's function for the heat conduction equation with small parameter”, Math. USSR-Sb., 16:2 (1972), 209–221
\Bibitem{Nes72}
\by G.~A.~Nesenenko
\paper On the asymptotic expansion of Green's function for the heat conduction equation with small parameter
\jour Math. USSR-Sb.
\yr 1972
\vol 16
\issue 2
\pages 209--221
\mathnet{http://mi.mathnet.ru/eng/sm3044}
\crossref{https://doi.org/10.1070/SM1972v016n02ABEH001421}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=303082}
\zmath{https://zbmath.org/?q=an:0243.35046|0248.35059}
Linking options:
https://www.mathnet.ru/eng/sm3044
https://doi.org/10.1070/SM1972v016n02ABEH001421
https://www.mathnet.ru/eng/sm/v129/i2/p204
This publication is cited in the following 6 articles:
Anosov A.A., Akimov A.I., Guzairov G.M., Rakityanskii A.S., “Chislennaya realizatsiya algoritma, osnovannogo na metode teplovykh potentsialov, primenitelno k singulyarno vozmuschennym zadacham teploprovodnosti”, Inzhenernaya fizika, 2009, no. 9, 3–7
A. A. Makarov, “Method of differential equations for the Renyi statistics”, J Math Sci, 41:1 (1988), 882
A. A. Makarov, “The Asymptotic Behavior of the Limit Distribution of the Kolmogorov–Smirnov Statistic in the Case of a Composite Hypothesis for the Class of Projecting Estimates of an Unknown Parameter”, Theory Probab Appl, 32:2 (1987), 380
Yu. N. Tyurin, “On the limit distribution of Kolmogorov–Smirnov statistics for a composite hypothesis”, Math. USSR-Izv., 25:3 (1985), 619–646
G. A. Nesenenko, Yu. N. Tyurin, “Ray asymptotics of the Green function for the heat equation with a small parameter”, Math. USSR-Sb., 52:2 (1985), 315–329
V. I. Kalinichenko, G. A. Nesenenko, “On an asymptotic of the solution of the first boundary-value problem of the heat-conduction equation with a nonstationary boundary”, Ukr Math J, 27:1 (1975), 70
Citation in format AMSBIB
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