Contractivity and Asymptotics in Wasserstein Metrics for Viscous Nonlinear Scalar Conservation Laws

José A. Carrillo; Marco Di Francesco; Corrado Lattanzio

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 2, page 277-292
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Carrillo, José A., Di Francesco, Marco, and Lattanzio, Corrado. "Contractivity and Asymptotics in Wasserstein Metrics for Viscous Nonlinear Scalar Conservation Laws." Bollettino dell'Unione Matematica Italiana 10-B.2 (2007): 277-292. <http://eudml.org/doc/290403>.

@article{Carrillo2007,
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-de- pendent asymptotic profiles for a large class of convection-diffusion problems with fully general nonlinearities and with degenerate diffusion.},
author = {Carrillo, José A., Di Francesco, Marco, Lattanzio, Corrado},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {277-292},
publisher = {Unione Matematica Italiana},
title = {Contractivity and Asymptotics in Wasserstein Metrics for Viscous Nonlinear Scalar Conservation Laws},
url = {http://eudml.org/doc/290403},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Carrillo, José A.
AU - Di Francesco, Marco
AU - Lattanzio, Corrado
TI - Contractivity and Asymptotics in Wasserstein Metrics for Viscous Nonlinear Scalar Conservation Laws
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/6//
PB - Unione Matematica Italiana
VL - 10-B
IS - 2
SP - 277
EP - 292
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-de- pendent asymptotic profiles for a large class of convection-diffusion problems with fully general nonlinearities and with degenerate diffusion.
LA - eng
UR - http://eudml.org/doc/290403
ER -

References

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