Abstract:
We consider the Cauchy problem for a certain class of anisotropic parabolic second-order equations with double non-power nonlinearities. The equation contains an “inhomogeneity” in the form of a non-divergent term depending on the sought function and spatial variables. Non-linearities are characterized by N-functions, for which Delta2-condition is not imposed. The uniqueness of renormalized solutions in Sobolev–Orlich spases is proved by the S. N. Kruzhkov method of doubling the variables.
Citation:
F. Kh. Mukminov, “Uniqueness of the renormalized solutions to the Cauchy problem for an anisotropic parabolic equation”, Ufa Math. J., 8:2 (2016), 44–57
\Bibitem{Muk16}
\by F.~Kh.~Mukminov
\paper Uniqueness of the renormalized solutions to the Cauchy problem for an anisotropic parabolic equation
\jour Ufa Math. J.
\yr 2016
\vol 8
\issue 2
\pages 44--57
\mathnet{http://mi.mathnet.ru/eng/ufa344}
\crossref{https://doi.org/10.13108/2016-8-2-44}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000411732200005}
\elib{https://elibrary.ru/item.asp?id=26255226}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84994353616}
Linking options:
https://www.mathnet.ru/eng/ufa344
https://doi.org/10.13108/2016-8-2-44
https://www.mathnet.ru/eng/ufa/v8/i2/p44
This publication is cited in the following 3 articles:
A. Aberqi, M. Elmassoudi, M. Hammoumi, “Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak-spaces”, Math. Model. Comput., 8:4 (2021), 584
A. Abercji, J. Bennouna, M. Elmassoudi, M. Hammoumi, “Existence and uniqueness of a renormalized solution of parabolic problems in Orlicz spaces”, Mon.heft. Math., 189:2 (2019), 195–219
V. F. Vil'danova, “Existence and uniqueness of a weak solution of a nonlocal aggregation equation with degenerate diffusion of general form”, Sb. Math., 209:2 (2018), 206–221
Citation in format AMSBIB
Contact us: