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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 1158–1173
DOI: https://doi.org/10.17377/semi.2018.15.094 (Mi semr985) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differentical equations, dynamical systems and optimal control

Anisotropic vanishing diffusion method applied to genuinely nonlinear forward-backward ultra-parabolic equations

I. V. Kuznetsovab, S. A. Sazhenkovba

a Novosibirsk State University, Pirogova st., 2, 630090, Novosibirsk, Russia
b Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, pr. Acad. Lavrentyeva 15, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/semi.2018.15.094
Abstract: The results formulated in (I.V. Kuznetsov, Sib. Elect. Math. Rep. 14 (2017), 710–731) are extended onto the multi-time case. We prove existence and uniqueness of kinetic solutions to genuinely nonlinear forward-backward ultra-parabolic equations and show that kinetic solutions do not depend on the anisotropic elliptic regularization.
Keywords: forward-backward ultra-parabolic equation, entropy solution, kinetic solution.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00649_a
Russian Academy of Sciences - Federal Agency for Scientific Organizations III.22.4.2
The work was supported by the Federal Agency for Scientific Organizations of the Russian Federation (project no. III.22.4.2) and by the Russian Foundation for Basic Research (grant no. 18-01-00649).
Received June 26, 2018, published October 15, 2018
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35K92
Language: English
Citation: I. V. Kuznetsov, S. A. Sazhenkov, “Anisotropic vanishing diffusion method applied to genuinely nonlinear forward-backward ultra-parabolic equations”, Sib. Èlektron. Mat. Izv., 15 (2018), 1158–1173
Citation in format AMSBIB
\Bibitem{KuzSaz18}
\by I.~V.~Kuznetsov, S.~A.~Sazhenkov
\paper Anisotropic vanishing diffusion method applied to genuinely nonlinear forward-backward ultra-parabolic equations
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1158--1173
\mathnet{http://mi.mathnet.ru/semr985}
\crossref{https://doi.org/10.17377/semi.2018.15.094}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000454860200036}
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