Global $BV$ Solutions for the P -System with Frictional Damping

Global $BV$ Solutions for the P -System with Frictional Damping

We construct global $BV$ solutions to the Cauchy problem for the damped $p$-system, under initial data with distinct end-states. The solution will be realized as a perturbation of its asymptotic profile, in which the specific volume satisfies the porous media equation and the velocity obeys the clas...

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Veröffentlicht in:SIAM journal on mathematical analysis 2009-01, Vol.41 (3), p.1190-1205
Hauptverfasser: Dafermos, Constantine M., Pan, Ronghua
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Asymptotic properties
Cauchy problem
Cauchy problems
Damping
Density
Gas flow
Gases
Law
Mathematical analysis
Perturbation methods
Velocity
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Zusammenfassung:We construct global $BV$ solutions to the Cauchy problem for the damped $p$-system, under initial data with distinct end-states. The solution will be realized as a perturbation of its asymptotic profile, in which the specific volume satisfies the porous media equation and the velocity obeys the classical Darcy law for gas flow through a porous medium.
ISSN:0036-1410
1095-7154
DOI:10.1137/080735126