Contractivity and asymptotics in wasserstein metrics for viscous nonlinear scalar conservation laws

J. A. Carrillo; M. Di Francesco; C. Lattanzio

Contractivity and asymptotics in wasserstein metrics for viscous nonlinear scalar conservation laws

J. A. Carrillo, M. Di Francesco, C. Lattanzio

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

4 Citations (Scopus)

Abstract

In this work, recent results concerning the long time asymptotics of one-dimensional scalar conservation laws with probability densities as initial data are reviewed and further applied to the case of viscous conservation laws with nonlinear degenerate diffusions. The non-strict contraction of the maximal transport distance together with a uniform expansion of the solutions lead to the existence of time-dependent asymptotic profiles for a large class of convection-diffusion problems with fully general nonlinearities and with degenerate diffusion.

Original language	English
Pages (from-to)	277-292
Journal	Bollettino della Unione Matematica Italiana B
Volume	10
Issue number	2
Publication status	Published - 1 Jun 2007

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title = "Contractivity and asymptotics in wasserstein metrics for viscous nonlinear scalar conservation laws",

abstract = "In this work, recent results concerning the long time asymptotics of one-dimensional scalar conservation laws with probability densities as initial data are reviewed and further applied to the case of viscous conservation laws with nonlinear degenerate diffusions. The non-strict contraction of the maximal transport distance together with a uniform expansion of the solutions lead to the existence of time-dependent asymptotic profiles for a large class of convection-diffusion problems with fully general nonlinearities and with degenerate diffusion.",

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AU - Carrillo, J. A.

AU - Di Francesco, M.

AU - Lattanzio, C.

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Y1 - 2007/6/1

N2 - In this work, recent results concerning the long time asymptotics of one-dimensional scalar conservation laws with probability densities as initial data are reviewed and further applied to the case of viscous conservation laws with nonlinear degenerate diffusions. The non-strict contraction of the maximal transport distance together with a uniform expansion of the solutions lead to the existence of time-dependent asymptotic profiles for a large class of convection-diffusion problems with fully general nonlinearities and with degenerate diffusion.

AB - In this work, recent results concerning the long time asymptotics of one-dimensional scalar conservation laws with probability densities as initial data are reviewed and further applied to the case of viscous conservation laws with nonlinear degenerate diffusions. The non-strict contraction of the maximal transport distance together with a uniform expansion of the solutions lead to the existence of time-dependent asymptotic profiles for a large class of convection-diffusion problems with fully general nonlinearities and with degenerate diffusion.

M3 - Article

VL - 10

SP - 277

EP - 292

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ER -