Volume 8, Issue 4
Global Perturbation of the Riemann Problem for the System of Compressible Flow Through Porous Media

Shaoqiang Tang & Ling Xiao

DOI:

J. Part. Diff. Eq., 8 (1995), pp. 351-370.

Published online: 1995-08

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  • 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.

  • Keywords

Hyperbolic Riemann problem perturbation global structure

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@Article{JPDE-8-351, author = {}, 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} }
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.
Shaoqiang Tang & Ling Xiao . (2019). Global Perturbation of the Riemann Problem for the System of Compressible Flow Through Porous Media. Journal of Partial Differential Equations. 8 (4). 351-370. doi:
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