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Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

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CARILLO, José A., Ansgar JÜNGEL, Peter A. MARKOVICH, Giuseppe TOSCANI, Andreas UNTERREITER, 1999. Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

@unpublished{Carillo1999Entro-6436, title={Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities}, year={1999}, author={Carillo, José A. and Jüngel, Ansgar and Markovich, Peter A. and Toscani, Giuseppe and Unterreiter, Andreas} }

Toscani, Giuseppe 1999 Jüngel, Ansgar Carillo, José A. Carillo, José A. Unterreiter, Andreas Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities 2011-03-24T16:12:42Z Unterreiter, Andreas deposit-license We analyse the large-time asymptotics of quasilinear (possibly) degenerate parabolic systems in three cases: 1) scalar problems with confinement by a uniformly convex potential, 2) unconfined scalar equations and 3) unconfined systems. In particular we are interested in the rate of decay to equilibrium or self-similar solutions. The main analytical tool is based on the analysis of the entropy dissipation. In the scalar case this is done by proving decay of the entropy dissipation rate and bootstrapping back to show convergence of the relative entropy to zero. As by-product, this<br />approach gives generalized Sobolev-inequalities, which interpolate between the Gross logarithmic Sobolev inequality and the classical Sobolev inequality.<br />The time decay of the solutions of the degenerate systems is analyzed by means of a generalisation of the Nash inequality. Porous media, fast diffusion, p-Laplace and energy transport systems are included in the considered class of problems. A generalized Csizar-Kullback inequality allows for an estimation of the decay to equilibrium in terms of the relative entropy. Toscani, Giuseppe eng Markovich, Peter A. application/pdf 2011-03-24T16:12:42Z Jüngel, Ansgar Markovich, Peter A.

Dateiabrufe seit 01.10.2014 (Informationen über die Zugriffsstatistik)

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