Solution of a two-dimensional parabolic model problem in a degenerate angular domain
Бұрыштық жойылатын облыста модельдiк екi өлшемдi параболалық есептi шешу
Решение модельной двумерной параболической задачи в угловой вырождающейся области
Ramazanov M.I. Gulmanov N.K. Kopbalina S.S.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#111Issue 391 - 108 pp.
In this paper, the boundary value problem of heat conduction in a domain was considered, boundary of which changes with time, as well as there is no the problem solution domain at the initial time, that is, it degenerates into a point. To solve the problem, the method of heat potentials was used, which makes it possible to reduce it to a singular Volterra type integral equations of the second kind. The peculiarity of the obtained integral equation is that it fundamentally differs from the classical Volterra integral equations, since the Picard method is not applicable to it and the corresponding homogeneous integral equation has a nonzero solution.
boundary value problem , degenerate domain , heat equation , regularization , Volterra singular integral equation
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Karaganda University of the Name of Academician E.A. Buketov, Karaganda, Kazakhstan
Karaganda University of the Name of Academician E.A. Buketov
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