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

Constantine M. Dafermos, Ronghua Pan
2009 SIAM Journal on Mathematical Analysis  
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.
doi:10.1137/080735126 fatcat:mfqvqgttm5hsrlcret5cxeldjy