@Article{JPDE-8-351, author = {Shaoqiang Tang and Ling Xiao }, title = {Global Perturbation of the Riemann Problem for the System of Compressible Flow Through Porous Media}, journal = {Journal of Partial Differential Equations}, year = {1995}, volume = {8}, number = {4}, pages = {351--370}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5667.html} }