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Existence and Asymptotic Behavior of Measure-Valued Solutions for Degenerate Conservation Laws

✍ Scribed by Gui-Qiang Chen; Hermano Frid

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 887 KB
Volume: 127
Category: Article
ISSN: 0022-0396
DOI: 10.1006/jdeq.1996.0068

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✦ Synopsis

We consider two classes of typical degenerate hyperbolic systems of conservation laws to provide a general approach for solving the existence and large-time asymptotic behavior of measure-valued solutions for initial-boundary value problems. Some existence theorems of the measure-valued solutions are established. The convergence of large time-averages of the measure-valued solutions to a Dirac mass, concentrated at the input state on the boundary, is proved for almost each fixed space variable. Although the measure-valued solutions of the initial-boundary problems may not be unique in general, our results indicate that the asymptotic equilibrium of these measure-valued solutions is unique.

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