Abstract:
A mixed problem for an equation of heat transfer with involution is considered. The uniqueness of the problem's solution is proved. The ill-posedness of the mixed problem with Dirichlet-type boundary conditions for this equation is shown. By application of Fourier method, we obtain a spectral problem for a second-order differential operator with involution with an infinite number of positive and negative eigenvalues. The Green function of obtained second-order differential operator with involution is constructed. Uniform estimate of the Green's function is established for sufficiently large values of the spectral parameter. The existence of the Green's function of a second-order differential operator with involution and with variable coefficient is proved. By estimation of the Green's function completeness of the eigenfunctions's system for operator discussed is proved. In the class of polynomials the existence of a solution of this ill-posed problem is proved.
\Bibitem{Sar19}
\by A.~A.~Sarsenbi
\paper The ill-posed problem for the heat transfer equation with involution
\jour Zhurnal SVMO
\yr 2019
\vol 21
\issue 1
\pages 48--59
\mathnet{http://mi.mathnet.ru/svmo726}
\crossref{https://doi.org/10.15507/2079-6900.21.201901.48-59}
Linking options:
https://www.mathnet.ru/eng/svmo726
https://www.mathnet.ru/eng/svmo/v21/i1/p48
This publication is cited in the following 4 articles:
Ya. O. Baranetskij, I. I. Demkiv, P. I. Kaleniuk, “Inverse Problems of Determination of the Time-Dependent Coefficient of a Parabolic Equation with Involution and Antiperiodicity Conditions”, J Math Sci, 282:5 (2024), 699
A. I. Kozhanov, O. I. Bzheumikhova, “Sobstvennye funktsii i sobstvennye chisla differentsialnykh uravnenii s involyutsiei”, Sib. matem. zhurn., 65:5 (2024), 953–964
Ya. O. Baranetskij, I. I. Demkiv, P. I. Kalenyuk, “Inverse problems of determination of a time-dependent coefficient of parabolic equation with involution and anti-periodicity conditions”, Mat. Met. Fiz. Mekh. Polya, 65:1-2 (2022)
Aleksandr I. Kozhanov, Oksana I. Bzheumikhova, “Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives”, Mathematics, 10:18 (2022), 3325
Citation in format AMSBIB
Contact us: