Geodesic
Estimates of the Nash--Aronson type for degenerating parabolic equations
Contemporary Mathematics. Fundamental Directions, Partial differential equations, Tome 39 (2011), pp. 66-78.

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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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     author = {V. V. Zhikov},
     title = {Estimates of the {Nash--Aronson} type for degenerating parabolic equations},
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     url = {http://geodesic.mathdoc.fr/item/CMFD_2011_39_a3/}
}
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V. V. Zhikov. Estimates of the Nash--Aronson type for degenerating parabolic equations. Contemporary Mathematics. Fundamental Directions, Partial differential equations, Tome 39 (2011), pp. 66-78. http://geodesic.mathdoc.fr/item/CMFD_2011_39_a3/

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