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CMFD, 2011, Volume 39, Pages 66–78 (Mi cmfd173)  

Estimates of the Nash–Aronson type for degenerating parabolic equations

V. V. Zhikov

Vladimir

Abstract: We consider second-order parabolic equations describing diffusion with degeneration and diffusion on singular and combined structures. We give a united definition of a solution of the Cauchy problem for such equations by means of semigroup theory in the space $L^2$ with a suitable measure. We establish some weight estimates for solutions of Cauchy problems. Estimates of Nash–Aronson type for the fundamental solution follow from them. We plan to apply these estimates to known asymptotic diffusion problems, namely, to the stabilization of solutions and to the “central limit theorem”.

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English version:
Journal of Mathematical Sciences, 2013, 190:1, 66–79

Bibliographic databases:

Document Type: Article
UDC: 517.956.4

Citation: V. V. Zhikov, “Estimates of the Nash–Aronson type for degenerating parabolic equations”, Partial differential equations, CMFD, 39, PFUR, M., 2011, 66–78; Journal of Mathematical Sciences, 190:1 (2013), 66–79

Citation in format AMSBIB
\Bibitem{Zhi11}
\by V.~V.~Zhikov
\paper Estimates of the Nash--Aronson type for degenerating parabolic equations
\inbook Partial differential equations
\serial CMFD
\yr 2011
\vol 39
\pages 66--78
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd173}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2830677}
\transl
\jour Journal of Mathematical Sciences
\yr 2013
\vol 190
\issue 1
\pages 66--79
\crossref{https://doi.org/10.1007/s10958-013-1246-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874945790}


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