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Siberian Journal of Pure and Applied Mathematics, 2016, Volume 16, Issue 2, Pages 6–15
DOI: https://doi.org/10.17377/PAM.2016.16.201 (Mi vngu398) 		 
A modified Galerkin method for semilinear parabolic equation with changing time direction

I. E. Egorov, E. S. Efimova

Institute for Mathematics and Informatics, North-Eastern Federal University
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DOI: https://doi.org/10.17377/PAM.2016.16.201
Abstract: In this work, to prove the unique solvability of the first boundary value problem for semilinear parabolic equation of second order with changing time direction a modified Galerkin method is applied and also regularization method is used. For the approximate solutions of the problem error estimate of the modified Galerkin method is set using the regularization parameter and eigenvalue of the spectral Dirichlet problem for the Laplace equation in the space variables.
Keywords: semilinear parabolic equation, boundary value problem, a priori estimate, inequality, error estimate.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 3047
Received: 20.12.2015
English version:
Journal of Mathematical Sciences, 2018, Volume 228, Issue 4, Pages 372–379
DOI: https://doi.org/10.1007/s10958-017-3628-5
Document Type: Article
UDC: 517.95
Language: Russian
Citation: I. E. Egorov, E. S. Efimova, “A modified Galerkin method for semilinear parabolic equation with changing time direction”, Sib. J. Pure and Appl. Math., 16:2 (2016), 6–15; J. Math. Sci., 228:4 (2018), 372–379
Citation in format AMSBIB
\Bibitem{EgoEfi16}
\by I.~E.~Egorov, E.~S.~Efimova
\paper A modified Galerkin method for semilinear parabolic equation with changing time direction
\jour Sib. J. Pure and Appl. Math.
\yr 2016
\vol 16
\issue 2
\pages 6--15
\mathnet{http://mi.mathnet.ru/vngu398}
\crossref{https://doi.org/10.17377/PAM.2016.16.201}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 228
\issue 4
\pages 372--379
\crossref{https://doi.org/10.1007/s10958-017-3628-5}
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