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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 139, Pages 44–58 (Mi into223)  
This article is cited in 1 scientific paper (total in 1 paper)

Existence of weak solutions to an elliptic-parabolic equation with variable order of nonlinearity

F. Kh. Mukminova, È. R. Andriyanovabc

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
b Australian Mathematical Sciences Institute, Melbourne, Australia
c Australian National University, Melbourne, Australia
Full-text PDF (229 kB) Citations (1)
Abstract: We consider an equation with variable nonlinearity of the form $|u|^{p(x)}$, in which the parabolic term can vanish, i.e., in the corresponding domain the parabolic equation becomes “elliptic.” Under a weak monotonicity conditions (nonstrict inequality) we prove the existence of a solution to the first mixed problem in a cylinder with a bounded base.
Keywords: weak solution, elliptic-parabolic equation, variable nonlinearity, existence of solutions.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-07920-а
The work of F. Kh. Mukminov was partially supported by the Russian Foundation for Basic Research (project No. 15-01-07920-a).
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 3, Pages 290–305
DOI: https://doi.org/10.1007/s10958-019-04424-5
Bibliographic databases:
Document Type: Article
UDC: 517.954, 517.956.45, 517.958:531.72
MSC: 35K20, 35D30, 35K55, 35K65
Language: Russian
Citation: F. Kh. Mukminov, È. R. Andriyanova, “Existence of weak solutions to an elliptic-parabolic equation with variable order of nonlinearity”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 139, VINITI, M., 2017, 44–58; Journal of Mathematical Sciences, 241:3 (2019), 290–305
Citation in format AMSBIB
\Bibitem{MukAnd17}
\by F.~Kh.~Mukminov, \`E.~R.~Andriyanova
\paper Existence of weak solutions to an elliptic-parabolic equation with variable order of nonlinearity
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 139
\pages 44--58
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into223}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3799905}
\zmath{https://zbmath.org/?q=an:1427.35140}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 3
\pages 290--305
\crossref{https://doi.org/10.1007/s10958-019-04424-5}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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