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Contemporary Mathematics. Fundamental Directions, 2010, Volume 36, Pages 12–23 (Mi cmfd152)  

This article is cited in 4 scientific papers (total in 4 papers)

Solutions in Hölder spaces of boundary-value problems for parabolic equations with nonconjugate initial and boundary data

G. I. Bizhanova

Institute of Mathematics, Ministry of Education and Science of the Republic of Kazakhstan, Almaty
Full-text PDF (189 kB) Citations (4)
References:
Abstract: The first and second one-dimensional boundary-value problems for parabolic equations are investigated in the case where the conjugation conditions for all required orders are not satisfied. The existence and uniqueness are proved. Estimates of solutions in classical and weighted Hölder spaces are obtained. We prove that the violation of conjugation for the given functions on the boundary of the domain at the initial-time moment causes the appearance of singular solutions. The order of singularity (as a power of $t$) is found for the singular solutions for $t=0$.
English version:
Journal of Mathematical Sciences, 2010, Volume 171, Issue 1, Pages 9–21
DOI: https://doi.org/10.1007/s10958-010-0122-8
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: G. I. Bizhanova, “Solutions in Hölder spaces of boundary-value problems for parabolic equations with nonconjugate initial and boundary data”, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, CMFD, 36, PFUR, M., 2010, 12–23; Journal of Mathematical Sciences, 171:1 (2010), 9–21
Citation in format AMSBIB
\Bibitem{Biz10}
\by G.~I.~Bizhanova
\paper Solutions in H\"older spaces of boundary-value problems for parabolic equations with nonconjugate initial and boundary data
\inbook Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17--24, 2008). Part~2
\serial CMFD
\yr 2010
\vol 36
\pages 12--23
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd152}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2752646}
\transl
\jour Journal of Mathematical Sciences
\yr 2010
\vol 171
\issue 1
\pages 9--21
\crossref{https://doi.org/10.1007/s10958-010-0122-8}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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