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This article is cited in 2 scientific papers (total in 2 papers)
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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Journal of Mathematical Sciences, 2013, 190:1, 66–79
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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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874945790}
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http://mi.mathnet.ru/eng/cmfd173 http://mi.mathnet.ru/eng/cmfd/v39/p66
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Qian Zh., Xi G., “Parabolic Equations With Divergence-Free Drift in Space (Ltlxq)-l-l”, Indiana Univ. Math. J., 68:3 (2019), 761–797
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Andres S., Deuschel J.-D., Slowik M., “Heat Kernel Estimates and Intrinsic Metric For Random Walks With General Speed Measure Under Degenerate Conductances”, Electron. Commun. Probab., 24 (2019), 5
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