Solution of the boundary value problem of heat conduction in a cone

• Autorzy: Ramazanov Murat , Jenaliyev Muvasharkhan , Gulmanov Nurtay

Identyfikatory

DOI

10.7494/OpMath.2022.42.1.75

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

non-cylindrical domain; cone; boundary value problem of heat conduction; singular Volterra integral equation; Carleman–Vekua regularization method

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2022
• Tom: Vol. 42, no. 1
• Strony: 75--91
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Ramazanov Murat

• Academician E.A. Buketov Karaganda State University, University Str. 28, 100028 Karaganda, Republic of Kazakhstan

• https://orcid.org/0000-0002-2297-5488

autor

Jenaliyev Muvasharkhan

• Institute of Mathematics and Mathematical Modeling, Pushkin Str. 125, 050010 Almaty, Republic of Kazakhstan

• https://orcid.org/0000-0001-8743-7026

autor

Gulmanov Nurtay

• Academician E.A. Buketov Karaganda State University, University Str. 28, 100028 Karaganda, Republic of Kazakhstan

• https://orcid.org/0000-0002-4159-1551

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).