Abstract:
In a degenerate domain, namely, the inverted cone, we consider a boundary value problem of heat conduction. For this problem the solvability theorems are established in weighted spaces of essentially bounded functions. The proofs of the theorems are based on the results of the solvability for a nonhomogeneous integral equation of the third kind. The problem under study is reduced to the study of this integral equation using the representation of the solution to the boundary value problem in the form of a sum of constructed thermal potentials.
Keywords and phrases:
fundamental solution, axial symmetry, modified Bessel function.
This work was supported by the Committee of Science of the Ministry of Education and Science of
the Republic of Kazakhstan (grants no. AP05132262 and AP05130928).
Citation:
M. T. Jenaliyev, M. I. Ramazanov, M. T. Kosmakova, Zh. M. Tuleutaeva, “On the solution to a two-dimensional heat conduction problem in a degenerate domain”, Eurasian Math. J., 11:3 (2020), 89–94
\Bibitem{DzhRamKos20}
\by M.~T.~Jenaliyev, M.~I.~Ramazanov, M.~T.~Kosmakova, Zh.~M.~Tuleutaeva
\paper On the solution to a two-dimensional heat conduction problem in a degenerate domain
\jour Eurasian Math. J.
\yr 2020
\vol 11
\issue 3
\pages 89--94
\mathnet{http://mi.mathnet.ru/emj377}
\crossref{https://doi.org/10.32523/2077-9879-2020-11-3-89-94}
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Linking options:
https://www.mathnet.ru/eng/emj377
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This publication is cited in the following 8 articles:
B. I. Islomov, D. A. Nasirova, “A problem with gellerstedt conditions on different characteristics for a mixed loaded equation of the second kind”, Eurasian Math. J., 15:1 (2024), 34–48
M. T. Kosmakova, A. N. Khamzeeva, “O razreshimosti integralnogo uravneniya, svyazannogo s drobno-nagruzhennoi zadachei teploprovodnosti”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach.
Pontryaginskie chteniya—XXXIV», Voronezh, 3-9 maya 2023 g. Chast 4, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 233, VINITI RAN, M., 2024, 27–36
Minzilya Kosmakova, Danna Akhmanova, Kamila Izhanova, Kareem T. Elgindy, “BVP with a Load in the Form of a Fractional Integral”, International Journal of Mathematics and Mathematical Sciences, 2024 (2024), 1
Minzilya KOSMAKOVA, Aleksandr AKHMETSHİN, “On the unique solvability of a Cauchy problem with a fractional derivative”, Advances in the Theory of Nonlinear Analysis and its Application, 7:1 (2023), 232
S. A. Budochkina, H. P. Vu, “On an indirect representation of evolutionary equations in the form of Birkhoff's equations”, Eurasian Math. J., 13:3 (2022), 23–32
M. T. Jenaliyev, M. T. Kosmakova, Zh. M. Tuleutaeva, “On the Solvability of Heat Boundary Value Problems in Sobolev Spaces”, Lobachevskii J Math, 43:8 (2022), 2133
M. T. Jenaliyev, M. I. Ramazanov, M. G. Yergaliyev, “On an inverse problem for a parabolic equation in a degenerate angular domain”, Eurasian Math. J., 12:2 (2021), 25–38
M. I. Ramazanov, M. T. Kosmakova, Zh. M. Tuleutaeva, “On the Solvability of the Dirichlet Problem for the Heat Equation in a Degenerating Domain”, Lobachevskii J Math, 42:15 (2021), 3715
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