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Initial-Boundary Value Problem for a Heat Equation with not Strongly Regular Boundary Conditions

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Functional Analysis in Interdisciplinary Applications (FAIA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 216))

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Abstract

We consider a problem on finding a solution of an initial-boundary value problem for a heat equation with regular, but not strongly regular boundary conditions. It is shown that in the case of the potential parity \(q(x)=q(1-x)\) the researched class of problems can always be reduced to a sequential solution of two analogous problems, but with strongly regular boundary conditions. Herewith the proof does not depend on whether the system of eigen- and associated functions of a corresponding spectral problem for an ordinary differential equation arising in applying the Fourier method forms a basis. The suggested way of the problem solution can be applied for constructing as classical, and for various types of generalized solutions. The solution method earlier suggested by the author is modernized. Due to this fact input data of the problem do not require an additional smoothness.

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Acknowledgements

The author expresses his great gratitude to the academician of RAS E.I. Moiseev and the academician of NAS RK T.Sh. Kal’menov for consistent support and fruitful discussion of the results. This research is supported by the grant no. 0824/GF4 and target program 0085/PTSF-14 of the Ministry of Education and Science of Republic of Kazakhstan.

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Authors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, 125 Pushkin st., Almaty, 050010, Kazakhstan

    Makhmud A. Sadybekov

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  1. Makhmud A. Sadybekov
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Correspondence to Makhmud A. Sadybekov .

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Editors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Tynysbek Sh. Kalmenov

  2. Department of Mechanics and Mathematics, Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan

    Erlan D. Nursultanov

  3. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

  4. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Makhmud A. Sadybekov

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Sadybekov, M.A. (2017). Initial-Boundary Value Problem for a Heat Equation with not Strongly Regular Boundary Conditions. In: Kalmenov, T., Nursultanov, E., Ruzhansky, M., Sadybekov, M. (eds) Functional Analysis in Interdisciplinary Applications. FAIA 2017. Springer Proceedings in Mathematics & Statistics, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-67053-9_32

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