Geodesic
Contractivity and Asymptotics in Wasserstein Metrics for Viscous Nonlinear Scalar Conservation Laws
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 2, pp. 277-292 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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-de- pendent asymptotic profiles for a large class of convection-diffusion problems with fully general nonlinearities and with degenerate diffusion. 
@article{BUMI_2007_8_10B_2_a1,
     author = {Carrillo, Jos\'e A. and Di Francesco, Marco and Lattanzio, Corrado},
     title = {Contractivity and {Asymptotics} in {Wasserstein} {Metrics} for {Viscous} {Nonlinear} {Scalar} {Conservation} {Laws}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {277--292},
     year = {2007},
     volume = {Ser. 8, 10B},
     number = {2},
     zbl = {1178.35390},
     mrnumber = {2339442},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_2_a1/}
}
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Carrillo, José A.; Di Francesco, Marco; Lattanzio, Corrado. Contractivity and Asymptotics in Wasserstein Metrics for Viscous Nonlinear Scalar Conservation Laws. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 2, pp. 277-292. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_2_a1/