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

Shaoqiang Tang & Ling Xiao

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 = {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} }
TY - JOUR T1 - Global Perturbation of the Riemann Problem for the System of Compressible Flow Through Porous Media AU - Shaoqiang Tang & Ling Xiao 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 and Ling Xiao . (1995). 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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