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On many-valued solutions of two-dimensional linear parabolic equations

TitleOn many-valued solutions of two-dimensional linear parabolic equations
AuthorsV. M. Zhuravlev1, V. M. Morozov2
1Ulyanovsk State University
2Technological Research Institute of Ulyanovsk State University
AnnotationThe problem of calculating solutions of two-dimensional linear parabolic equations is considered. A complete procedure for the derivation of solutions is presented and the appearance of a specific degeneracy, called a topological one, is shown. It is shown that, in a two-dimensional coordinate space, among the parabolic equations with topological degeneracy, there is the Schrödinger equation for a nonstationary quantum harmonic oscillator, a homogeneous electric field, and an empty space. Examples of specific solutions are given.
KeywordsExact solutions of linear two-dimensional parabolic equations, multivalued solutions, two-dimensional quantum oscillator
CitationZhuravlev V. M., Morozov V. M. ''On many-valued solutions of two-dimensional linear parabolic equations'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 330-340. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper46.pdf. - Date of access: 24.08.2019.