Singularly perturbed multidimensional parabolic equation with rapidly oscillating free term
Abstract
UDC 517.9
The regularized asymptotics of a solution of the first boundary value problem for a two-dimensional differential equation of parabolic type is constructed when the phase derivative vanishes at one point. It is shown that angular and multidimensional boundary layer functions appear in such problems in addition to other boundary layers.
References
S. F. Feshchenko, N. Y. Shkyl, L. D. Nykolaenko, Asymptotycheskye metody v teoryy lyneinykh dyfferentsyalnykh uravnenyi, Kyev (1966).
S. A. Lomov, Y. S. Lomov, Osnovy matematycheskoi teoryy pohranychnoho sloia, Yzd-vo Mosk. hos. un-ta, Moskva (2011).
A. S. Omuralyev, Asymptotyka reshenyia synhuliarno vozmushchennыkh parabolycheskykh zadach, Lambert Acad. Publ. (2017).
Asan Omuraliev, Ella Abylaeva, Asymptotics of the solution of parabolic problems with multipoint stationary phase, AIP Conf. Proc. 1880, 1 – 6 (2017); http://dx.doi.org/10.1063/1.5000623. DOI: https://doi.org/10.1063/1.5000623
Asan Omuraliev, Ella Abylaeva, Asymptotyka reshenyia parabolycheskoi zadachy so statsyonarnoi fazoi, Yssledovanyia po yntehro-dyfferentsyalnym uravnenyiam, vyp. 47, 120 – 127 (???).
A. B. Vasyleva, V. F. Butuzov, Asymptotycheskye metody v teoryy synhuliarnykh vozmushchenyi, Vyssh. shk., Moskva (1990).
A. S. Omuralyev, M. Ymash kyzy, Synhuliarno vozmushchennaia parabolycheskaia zadacha s mnohomernymy pohranychnymy sloiamy, Dyfferents. uravnenyia, 13, № 12, 1664 – 1678 (2017).
O. A. Ladyzhenskaia, V. A. Solonnykov, N. N. Uraltseva, Lyneinye y kvazylyneinye uravnenyia parabolycheskoho typa, Nauka, Moskva (1967).
A. D. Polianyn, Spravochnyk po lyneinym uravnenyiam matematycheskoi fyzyky, Fyzmatlyt, Moskva (2001).
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