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ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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MSC2010 34М03, 34L10

The ill-posed problem for the heat transfer equation with involution

A. A. Sarsenbi1

AnnotationA 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.
Keywordsdifferential equation with involution, Fourier method, Green's function, eigenfunctions, basis

1Abdisalam A. Sarsenbi, doctoral candidate of Department of Mathematics, M. Auezov South Kazakhstan State University (5 Taukehan Av., Shymkent 160012, Kazakhstan), ORCID: https://orcid.org/0000-0002-1667-3010, abdisalam@mail.ru

Citation: A. A. Sarsenbi, "[The ill-posed problem for the heat transfer equation with involution]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,21:1 (2019) 48–59 (In Russian)

DOI 10.15507/2079-6900.21.201901.48-59