TY - JOUR
T1 - Global Perturbation of the Riemann Problem for the System of Compressible Flow Through Porous Media
JO - Journal of Partial Differential Equations
VL - 4
SP - 351
EP - 370
PY - 1995
DA - 1995/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5667.html
KW - Hyperbolic
KW - Riemann problem
KW - perturbation
KW - global structure
AB -  In this paper we consider the unperturbatcd and perturbated Riemann problem for the damped quasiliuear hyperbolic system {v_t - u_x = 0 u_t + p(v)_x = -αu, α > 0, p'(v} < 0 with initial structure of two rarefaction waves or one rarefaction wave plus one shock wave. Under certain restrictions, it admits a unique global discontinuous solution in a class of piecewise continuous and piecewise smooth functions and keeps the initial structure. Moreover, the shock strength is found decaying exponentially due to damping for the later case.