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

Title	On many-valued solutions of two-dimensional linear parabolic equations
Authors	V. M. Zhuravlev¹, V. M. Morozov² ¹Ulyanovsk State University ²Technological Research Institute of Ulyanovsk State University
Annotation	The 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.
Keywords	Exact solutions of linear two-dimensional parabolic equations, multivalued solutions, two-dimensional quantum oscillator
Citation	Zhuravlev 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: https://conf.svmo.ru/files/deamm2017/papers/paper46.pdf. - Date of access: 19.04.2024.