The L1-Stability of Boundary Layers for Scalar Viscous Conservation Laws.
In: Journal of Dynamics & Differential Equations, Jg. 13 (2001-10-01), Heft 4, S. 745-755
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Zugriff:
Let v= v( x) be a non-trivial bounded steady solution of a viscous scalar conservation law u t + f( u) x = u xx on a half-line R + , with a Dirichlet boundary condition. The semi-group of this IBVP is known to be contractive for the distance d( u, u′)≔| u− u′| 1 induced by L 1 (R + ). We prove here that v is asymptotically stable with respect to d: if u 0 − v∈ L 1 , then | u( t)− v| 1 →0 as t→+∞. When v is a constant, we show that this property holds if and only if f′( v)≤0. These results complement our study of the Cauchy problem [2]. [ABSTRACT FROM AUTHOR]
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Titel: |
The L1-Stability of Boundary Layers for Scalar Viscous Conservation Laws.
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Autor/in / Beteiligte Person: | Freistühler, Heinrich ; Serre, Denis |
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Zeitschrift: | Journal of Dynamics & Differential Equations, Jg. 13 (2001-10-01), Heft 4, S. 745-755 |
Veröffentlichung: | 2001 |
Medientyp: | academicJournal |
ISSN: | 1040-7294 (print) |
DOI: | 10.1023/A:1016646026758 |
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