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Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images. / Vaskevich, V. L.; Wenyuan, Yan.

In: Lobachevskii Journal of Mathematics, Vol. 46, No. 9, 09.2025, p. 4534-4542.

Research output: Contribution to journal › Article › peer-review

Harvard

Vaskevich, VL & Wenyuan, Y 2025, 'Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images', Lobachevskii Journal of Mathematics, vol. 46, no. 9, pp. 4534-4542. https://doi.org/10.1134/S1995080225612020

APA

Vaskevich, V. L., & Wenyuan, Y. (2025). Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images. Lobachevskii Journal of Mathematics, 46(9), 4534-4542. https://doi.org/10.1134/S1995080225612020

Vancouver

Vaskevich VL, Wenyuan Y. Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images. Lobachevskii Journal of Mathematics. 2025 Sept;46(9):4534-4542. doi: 10.1134/S1995080225612020

Author

Vaskevich, V. L. ; Wenyuan, Yan. / Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images. In: Lobachevskii Journal of Mathematics. 2025 ; Vol. 46, No. 9. pp. 4534-4542.

BibTeX

@article{0f519f78083a41e8b988a6f8c60101ec,
title = "Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images",
abstract = "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.",
keywords = "Fourier image, integral operator, integrodifferential equation, quadratic nonlinearity, quasilinear heat conduction equation",
author = "Vaskevich, {V. L.} and Yan Wenyuan",
note = "Vaskevich, V.L., Wenyuan, Y. Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images. Lobachevskii J Math 46, 4534–4542 (2025). https://doi.org/10.1134/S1995080225612020 This work was carried out as part of a state assignment for the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, project no. FWNF-2022-0008.",
year = "2025",
month = sep,
doi = "10.1134/S1995080225612020",
language = "English",
volume = "46",
pages = "4534--4542",
journal = "Lobachevskii Journal of Mathematics",
issn = "1995-0802",
publisher = "ФГБУ {"}Издательство {"}Наука{"}",
number = "9",

}

RIS

TY - JOUR

T1 - Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images

AU - Vaskevich, V. L.

AU - Wenyuan, Yan

N1 - Vaskevich, V.L., Wenyuan, Y. Cauchy Problem for the Quasilinear Heat Conduction Equation in Fourier Images. Lobachevskii J Math 46, 4534–4542 (2025). https://doi.org/10.1134/S1995080225612020 This work was carried out as part of a state assignment for the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, project no. FWNF-2022-0008.

PY - 2025/9

Y1 - 2025/9

N2 - 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.

AB - 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.

KW - Fourier image

KW - integral operator

KW - integrodifferential equation

KW - quadratic nonlinearity

KW - quasilinear heat conduction equation

UR - https://www.scopus.com/pages/publications/105027019110

UR - https://www.mendeley.com/catalogue/44ba3ce0-bebb-3b8c-ae8a-e4b65c94ad97/

U2 - 10.1134/S1995080225612020

DO - 10.1134/S1995080225612020

M3 - Article

VL - 46

SP - 4534

EP - 4542

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 9

ER -

ID: 74616853