EPJ Web Conf.
Volume 248, 2021V International Conference “Modeling of Nonlinear Processes and Systems“ (MNPS-2020)
|Number of page(s)||8|
|Section||Mathematical Models in Natural Sciences|
|Published online||26 April 2021|
Transmutation Operator Method for Solving Heat Conduction Problem
Moscow State Technological University “STANKIN “, RU-127055, Moscow, Russia
2 Penza State University, RU-440026, Penza, Russia
* Corresponding author: firstname.lastname@example.org
Published online: 26 April 2021
The transmutation operator method is extended to the case of functions of two variables. The transmutation operator flattens the function, i.e. the transmutation operator replaces a function with discontinuous partial derivatives on the coordinate axes by a continuously differentiable function. The work reveal the properties of the transmutation operator, and prove the commutativity of the transmutation operator and the Laplace operator. It was found that the Cauchy problem for the Laplace equation with internal conjugations in an unbounded domain can be replaced with the model Cauchy problem for the twodimensional Laplace equation. As a result, a new analytical method for solving initial-boundary value problems for a two-dimensional heat equation has been developed. The factorization of the transmutation operator is established as a product of two one-dimensional transmutation operators. The form of the transmutation operator establishing the isomorphism of two mathematical models of heat conduction in unbounded media with different physical characteristics was found and descrfibed.
© The Authors, published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.