Carrillo, Di Francesco, Lattanzio: Contractivity and Asymptotics in Wasserstein Metrics for Viscous Nonlinear Scalar Conservation Laws

Carrillo, José A. and Di Francesco, Marco and Lattanzio, Corrado:
Contractivity and Asymptotics in Wasserstein Metrics for Viscous Nonlinear Scalar Conservation Laws
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.2, p. 277-292, Unione Matematica Italiana (English)
pdf (429 Kb), djvu (156 Kb). | MR 2339442 | Zbl 1178.35390

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In questo articolo sono riportati alcuni risultati recenti riguardo il comportamento asintotico nel tempo di leggi di conservazione scalari in una dimensione spaziale e con densità di probabilità come dati iniziali. Tali risultati sono quindi applicati al caso di leggi di conservazione viscose con diffusioni nonlineari degeneri. Le proprietà di contrazione nella distanza di trasporto massimale e di uniforme espansione delle soluzioni forniscono l'esistenza di profili asintotici dipendenti dal tempo per un'ampia classe di equazioni di convenzione-diffusione con nonlinearità arbitrarie e diffusione degenere.

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Referenze Bibliografiche