Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images

Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images Full article

Journal

Lobachevskii Journal of Mathematics
ISSN: 1995-0802 , E-ISSN: 1818-9962

Output data

Year: 2025, Volume: 46, Number: 9, Pages: 4534-4542 Pages count : 9 DOI: 10.1134/s1995080225612020

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0008

In this paper, we consider the Cauchy problem for the quasilinear heat conduction equation with a variable heat capacity coefficient and a heat transfer coefficient proportional to temperature. The Cauchy problem for the original equation is reduced to a dual problem for some integro-differential equation for the Fourier image of the desired solution with initial data on the positive semi-axis. Integration in the obtained equation for the Fourier image of the solution to the initial differential problem is performed over the first quadrant of the plane of independent variables. The bilinear integral operator in the obtained integro-differential equation has as a kernel a function of frequency variable and two non-negative integration variables. The kernel is explicitly expressed through the variable heat capacity coefficient of the original differential equation.

Vaskevich V.L. , Yan W.
Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images
Lobachevskii Journal of Mathematics. 2025. V.46. N9. P.4534-4542. DOI: 10.1134/s1995080225612020 WOS Scopus OpenAlex

Submitted:	Mar 15, 2025
Accepted:	Jul 28, 2025
Published print:	Jan 10, 2026
Published online:	Jan 10, 2026

Web of science:	WOS:001659047600014
Scopus:	2-s2.0-105027019110
OpenAlex:	W7120037899

Пока нет цитирований