Two-Dimensional Boundary Value Problem of Heat Conduction in a Cone with Special Boundary Conditions

Ramazanov M.I. Jenaliyev M.T. Tanin A.O.
December 2021 Pleiades journals

Lobachevskii Journal of Mathematics
2021 #42 Issue 12 2913 - 2925 pp.

Abstract: We consider the boundary value problem of heat conduction in a domain that is an inverted cone, while the boundary conditions contain a derivative with respect to the time variable. 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 integral Volterra equation of the second kind, to which the original problem is reduced, are studied. Then we use the Carleman–Vekua regularization method to solve the resulting singular Volterra integral equation.

Bessel function , boundary value problem of heat conduction , Carleman–Vekua regularization method , singular Volterra integral equation , solvability

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Buketov Karaganda University, Karaganda, 100026, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 040500, Kazakhstan

Buketov Karaganda University
Institute of Mathematics and Mathematical Modeling

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