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

Abstract : e describe the asymptotic behavior as $t\to \infty$ of the solution of $u_t=\Delta_p u$ in $\R^N$, for $(2N+1)/(N+1)\le p < N$ and $L^1$ non-negative initial data. Optimal rates in $L^q$, $q=2-1/(p-1)$ for the convergence towards a self-similar profile corresponding to a solution with Dirac distribution initial data are found. They are connected with optimal constants for a Gagliardo-Nirenberg inequality.

 ASYMPTOTIC BEHAVIOR OF NONLINEAR DIFFUSIONS
 DEL PINO Manuel, DOLBEAULT Jean
2001-27
04-10-2001

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