SOLUTION OF THE BOUNDARY VALUE PROBLEM OF HEAT CONDUCTION IN A CONE
Ramazanov M. Jenaliyev M. Gulmanov N.
2022AGH University of Science and Technology
Opuscula Mathematica
2022#42Issue 175 - 91 pp.
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.
Boundary value problem of heat conduction , Carleman–Vekua regularization method , Cone , Noncylindrical domain , Singular Volterra integral equation
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Academician E.A. Buketov Karaganda State University, University Str. 28, Karaganda, 100028, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Pushkin Str. 125, Almaty, 050010, Kazakhstan
Academician E.A. Buketov Karaganda State University
Institute of Mathematics and Mathematical Modeling
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