Large time behaviour for degenerate parabolic equations with convection

Article type: Research Article

Authors: Andreucci, Daniele^; | Tedeev, Anatoli F.

Affiliations: Dipartimento di Metodi e Modelli, Università La Sapienza, via A. Scarpa 16, 00161 Roma, Italy. E-mail: andreucci@dmmm.uniroma1.it | Institute of Applied Mathematics, Academy of Sciences, Donetsk, Ukraine. E-mail: tedeev@iamm.ac.donetsk.ua

Note: [] The first author is member of Italian G.N.F.M.-I.N.d.A.M.

Abstract: We consider the Cauchy problem for a doubly nonlinear parabolic equation, obtaining optimal estimates both for the sup norm of nonnegative solutions, and for their support for large times.

Keywords: convection–diffusion equation, long-time behaviour, finite speed of propagation, entropy inequality

DOI: 10.3233/ASY-2008-0906

Journal: Asymptotic Analysis, vol. 60, no. 3-4, pp. 227-247, 2008