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Home » Issues » Archive of Issues » 2021 - 2 issue » pp. 241-252

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Kazakhstan Karaganda
Year
2021
Volume
31
Issue
2
Pages
241-252
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Section Mathematics
Title On the singular Volterra integral equation of the boundary value problem for heat conduction in a degenerating domain
Author(-s) Ramazanov M.I.a, Gulmanov N.K.a
Affiliations Karaganda State Universitya
Abstract In this paper, we consider a singular Volterra type integral equation of the second kind, to which some boundary value problems of heat conduction in domains with a boundary varying with time are reduced by the method of thermal potentials. The peculiarity of such problems is that the domain degenerates into a point at the initial moment of time. Accordingly, a distinctive feature of the integral equation under study is that the integral of the kernel, as the upper limit of integration tends to the lower one, is not equal to zero. This circumstance does not allow solving this equation by the method of successive approximations. We constructed the general solution of the corresponding characteristic equation and found the solution of the complete integral equation by the Carleman–Vekua method of equivalent regularization. It is shown that the corresponding homogeneous integral equation has a nonzero solution.
Keywords integral equation, a singular Volterra type integral equation of the second kind, Carleman–Vekua regularization method
UDC 517.968
MSC 45D05, 45E10
DOI 10.35634/vm210206
Received 20 April 2021
Language Russian
Citation Ramazanov M.I., Gulmanov N.K. On the singular Volterra integral equation of the boundary value problem for heat conduction in a degenerating domain, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 2, pp. 241-252.
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