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Asymptotic behavior for doubly degenerate parabolic equations

✍ Scribed by Martial Agueh

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
113 KB
Volume
337
Category
Article
ISSN
1631-073X

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✦ Synopsis

We use mass transportation inequalities to study the asymptotic behavior for a class of doubly degenerate parabolic equations of the form

where

We investigate the case where the potential V is uniformly c-convex, and the degenerate case where V = 0. In both cases, we establish an exponential decay in relative entropy and in the c-Wasserstein distance of solutions -or self-similar solutions -of (1) to equilibrium, and we give the explicit rates of convergence. In particular, we generalize to all p > 1, the HWI inequalities obtained by Otto and Villani (J. Funct. Anal. 173 (2) (2000) 361-400) when p = 2. This class of PDEs includes the Fokker-Planck, the porous medium, fast diffusion and the parabolic p-Laplacian equations.

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