A new mathematical model of heat conduction processes
type: Item
instance of: scholarly article
title: A new mathematical model of heat conduction processes
zbMATH Open document ID: 0711.35060
DOI: 10.1007/BF01071016
author: A. S. Galitsyn
author: A. S. Polubinskij
author: W. I. Fushchich
published in: Ukrainian Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: In the paper a fourth-order PDE invariant under the Galileo's group G(1,3) is studied. The equation has so called biparabolic form \(L(u)=\alpha_ 1L_ 1(u)+\alpha_ 2L_ 2(u)=0\), where \(L_ 2=L_ 1L_ 1\) and \(L_ 1\) is the classic heat conduction operator [see the author, Dokl. Akad. Nauk Ukr. SSR, Ser. A 1988, No.8, 22-27 (1988; Zbl 0682.35052)]. It is noted that this equation describes heat and diffusion processes in a more adequate way than hyperbolic heat equations. This comes from the fact that for most of the PDEs of second order with respect to time neither the Galileo's relativistic principle, nor the Poincaré-Einstein principle are fulfilled. An integral representation of the solution of a corresponding boundary value problem, as well as solutions of the Cauchy problem and of the travelling wave type are obtained. Also, a power boundary regime and some peaking mode [see, for example, \textit{A. A. Samarskij}, \textit{V. A. Galaktionov}, \textit{S. P. Kurdyumov} and \textit{A. P. Mikhajlov}, Processes with strain for quasilinear parabolic equations (Russian) (1987; Zbl 0631.35002)] are analyzed.
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 4169230
zbMATH Keywords: Galileo's group
zbMATH Keywords: biparabolic form
zbMATH Keywords: travelling wave
MaRDI profile type: Publication
cites work: Q5821083
cites work: The Galilean relativistic principle and nonlinear partial differential equations
cites work: Q5337507
cites work: Q3789180
full work available at URL: https://doi.org/10.1007/bf01071016
OpenAlex ID: W2077767313
description: scientific article; zbMATH DE number 4169230