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

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

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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 languageEnglish
Pages (from-to)277-292
JournalBollettino della Unione Matematica Italiana B
Volume10
Issue number2
Publication statusPublished - 1 Jun 2007

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