Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : Qualitative properties of nonnegative solutions to a quasilinear degenerate
parabolic equation with an absorption term depending solely on the
gradient are shown, providing information on the competition between
the nonlinear diffusion and the nonlinear absorption. In particular,
the limit as t goes to infinity of the $L^1$norm of integrable solutions is
identified, together with the rate of expansion of the support for
compactly supported initial data. The persistence of dead cores is
also shown. The proof of these results strongly relies on gradient
estimates which are first established. 





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