Abstract:
We prove that the operator of a boundary value problem of heat conduction in an infinite angular domain is Noetherian with index −1−1 in the class of growing functions.
Keywords:
heat conduction, Volterra equation, Abel equation, index.
Citation:
M. M. Amangalieva, M. T. Dzhenaliev, M. T. Kosmakova, M. I. Ramazanov, “On one homogeneous problem for the heat equation in an infinite angular domain”, Sibirsk. Mat. Zh., 56:6 (2015), 1234–1248; Siberian Math. J., 56:6 (2015), 982–995
\Bibitem{AmaDzhKos15}
\by M.~M.~Amangalieva, M.~T.~Dzhenaliev, M.~T.~Kosmakova, M.~I.~Ramazanov
\paper On one homogeneous problem for the heat equation in an infinite angular domain
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 6
\pages 1234--1248
\mathnet{http://mi.mathnet.ru/smj2709}
\crossref{https://doi.org/10.17377/smzh.2015.56.603}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3492902}
\elib{https://elibrary.ru/item.asp?id=24817516}
\transl
\jour Siberian Math. J.
\yr 2015
\vol 56
\issue 6
\pages 982--995
\crossref{https://doi.org/10.1134/S0037446615060038}
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Linking options:
https://www.mathnet.ru/eng/smj2709
https://www.mathnet.ru/eng/smj/v56/i6/p1234
This publication is cited in the following 34 articles:
M. T. Dzhenaliev, M. G. Ergaliev, A. A. Asetov, A. M. Ayazbaeva, “O zadache tipa Neimana dlya uravneniya Byurgersa v vyrozhdayuscheisya uglovoi oblasti”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 28 yanvarya – 2 fevralya 2021 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 206, VINITI RAN, M., 2022, 42–62
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, N. K. Gulmanov, “O singulyarnom integralnom uravnenii Volterra kraevoi zadachi teploprovodnosti v vyrozhdayuscheisya oblasti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:2 (2021), 241–252
Ramazanov I M., Jenaliyev M.T., Tanin A.O., “Two-Dimensional Boundary Value Problem of Heat Conduction in a Cone With Special Boundary Conditions”, Lobachevskii J. Math., 42:12 (2021), 2913–2925
Amangaliyeva M., Jenaliyev M., Iskakov S., Ramazanov M., “On a Boundary Value Problem For the Heat Equation and a Singular Integral Equation Associated With It”, Appl. Math. Comput., 399 (2021), 126009
Jenaliyev M.T., Ramazanov I M., Tanin A.O., “To the Solution of the Solonnikov-Fasano Problem With Boundary Moving on Arbitrary Law X = Gamma(T).”, Bull. Karaganda Univ-Math., 101:1 (2021), 37–49
M. T. Jenaliyev, A. A. Assetov, M. G. Yergaliyev, “On the Solvability of the Burgers Equation with Dynamic Boundary Conditions in a Degenerating Domain”, Lobachevskii J Math, 42:15 (2021), 3661
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
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
M. Jenaliyev, M. Ramazanov, M. Yergaliyev, “On the coefficient inverse problem of heat conduction in a degenerating domain”, Appl. Anal., 99:6 (2020), 1026–1041
D. M. Akhmanova, N. K. Shamatayeva, L. Zh. Kasymova, “On boundary value problems for essentially loaded parabolic equations in bounded domains”, Bull. Karaganda Univ-Math., 98:2 (2020), 6–14
M. T. Jenaliyev, M. I. Ramazanov, A. A. Assetov, “On Solonnikov-Fasano problem for the Burgers equation”, Bull. Karaganda Univ-Math., 98:2 (2020), 69–83
M. T. Kosmakova, V. G. Romanovski, D. M. Akhmanova, Zh. M. Tuleutaeva, A. Yu. Bartashevich, “On the solution to a two-dimensional boundary value problem of heat conduction in a degenerating domain”, Bull. Karaganda Univ-Math., 98:2 (2020), 100–109
M. T. Kosmakova, A. O. Tanin, Zh. M. Tuleutaeva, “Constructing the fundamental solution to a problem of heat conduction”, Bull. Karaganda Univ-Math., 97:1 (2020), 68–78
D. M. Akhmanova, M. T. Kosmakova, B. A. Shaldykova, “On strongly loaded heat equations”, Bull. Karaganda Univ-Math., 96:4 (2019), 8–14
M. T. Kosmakova, D. M. Akhmanova, Zh. M. Tuleutaeva, L. Zh. Kasymova, “Solving a nonhomogeneous integral equation with the variable lower limit”, Bull. Karaganda Univ-Math., 96:4 (2019), 52–57
M. T. Kosmakova, V. G. Romanovski, N. T. Orumbayeva, Zh. M. Tuleutaeva, L. Zh. Kasymova, “On the integral equation of an adjoint boundary value problem of heat conduction”, Bull. Karaganda Univ-Math., 95:3 (2019), 33–43
M. T. Kosmakova, D. M. Akhmanova, Zh. M. Tuleutaeva, L. Zh. Kasymova, “On a pseudo-Volterra nonhomogeneous integral equation”, Bull. Karaganda Univ-Math., 94:2 (2019), 48–55
M. T. Jenaliyev, M. I. Ramazanov, M. T. Kosmakova, A. O. Tanin, “To the solution of one pseudo-Volterra integral equation”, Bull. Karaganda Univ-Math., 93:1 (2019), 19–30
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