Open AccessSolution of the boundary value problem of heat conduction in a cone
Author(s) -
M.I. Ramazanov,
Muvasharkhan Jenaliyev,
N.K. Gulmanov
Publication year - 2022
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2022.42.1.75
Subject(s) - mathematics , boundary value problem , mathematical analysis , regularization (linguistics) , cone (formal languages) , bounded function , domain (mathematical analysis) , moment (physics) , volterra integral equation , integral equation , thermal conduction , heat equation , physics , algorithm , classical mechanics , artificial intelligence , computer science , materials science , composite material
In the paper we consider the boundary value problem of heat conduction in a non-cylindrical domain, which is an inverted cone, i.e. in the domain degenerating into a point at the initial moment of time. In this case, the boundary conditions contain a derivative with respect to the time variable; in practice, problems of this kind arise in the presence of the condition of the concentrated heat capacity. We prove a theorem on the solvability of a boundary value problem in weighted spaces of essentially bounded functions. The issues of solvability of the singular Volterra integral equation of the second kind, to which the original problem is reduced, are studied. We use the Carleman-Vekua method of equivalent regularization to solve the obtained singular Volterra integral equation.