# American Institute of Mathematical Sciences

September  2006, 1(3): 495-511. doi: 10.3934/nhm.2006.1.495

## A Well Posed Riemann Problem for the $p$--System at a Junction

 1 Department of Mathematics, University of Brescia, Via Branze, 38, 25133 Brescia, Italy 2 Department of Mathematics and Applications, University of Milano-Bicocca, Via R. Cozzi, 53, 20125 Milano, Italy

Received  March 2006 Revised  May 2006 Published  July 2006

This work is devoted to the solution to Riemann Problems for the $p$-system at a junction, the main goal being the extension to the case of an ideal junction of the classical results that hold in the standard case.
Citation: Rinaldo M. Colombo, Mauro Garavello. A Well Posed Riemann Problem for the $p$--System at a Junction. Networks & Heterogeneous Media, 2006, 1 (3) : 495-511. doi: 10.3934/nhm.2006.1.495
 [1] Lihui Guo, Wancheng Sheng, Tong Zhang. The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system$^*$. Communications on Pure & Applied Analysis, 2010, 9 (2) : 431-458. doi: 10.3934/cpaa.2010.9.431 [2] Matthias Hieber, Miho Murata. The $L^p$-approach to the fluid-rigid body interaction problem for compressible fluids. Evolution Equations & Control Theory, 2015, 4 (1) : 69-87. doi: 10.3934/eect.2015.4.69 [3] Qin Wang, Kyungwoo Song. The regularity of sonic curves for the two-dimensional Riemann problems of the nonlinear wave system of Chaplygin gas. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1661-1675. doi: 10.3934/dcds.2016.36.1661 [4] Jianjun Chen, Wancheng Sheng. The Riemann problem and the limit solutions as magnetic field vanishes to magnetogasdynamics for generalized Chaplygin gas. Communications on Pure & Applied Analysis, 2018, 17 (1) : 127-142. doi: 10.3934/cpaa.2018008 [5] Thibaut Allemand. Derivation of a two-fluids model for a Bose gas from a quantum kinetic system. Kinetic & Related Models, 2009, 2 (2) : 379-402. doi: 10.3934/krm.2009.2.379 [6] Paolo Secchi. An alpha model for compressible fluids. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 351-359. doi: 10.3934/dcdss.2010.3.351 [7] Chun Shen, Wancheng Sheng, Meina Sun. The asymptotic limits of solutions to the Riemann problem for the scaled Leroux system. Communications on Pure & Applied Analysis, 2018, 17 (2) : 391-411. doi: 10.3934/cpaa.2018022 [8] Tung Chang, Gui-Qiang Chen, Shuli Yang. On the 2-D Riemann problem for the compressible Euler equations I. Interaction of shocks and rarefaction waves. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 555-584. doi: 10.3934/dcds.1995.1.555 [9] Tung Chang, Gui-Qiang Chen, Shuli Yang. On the 2-D Riemann problem for the compressible Euler equations II. Interaction of contact discontinuities. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 419-430. doi: 10.3934/dcds.2000.6.419 [10] Zhenhua Guo, Wenchao Dong, Jinjing Liu. Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids. Communications on Pure & Applied Analysis, 2019, 18 (4) : 2133-2161. doi: 10.3934/cpaa.2019096 [11] Lihui Guo, Tong Li, Gan Yin. The vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term. Communications on Pure & Applied Analysis, 2017, 16 (1) : 295-310. doi: 10.3934/cpaa.2017014 [12] Dariusz Idczak, Rafał Kamocki. Existence of optimal solutions to lagrange problem for a fractional nonlinear control system with riemann-liouville derivative. Mathematical Control & Related Fields, 2017, 7 (3) : 449-464. doi: 10.3934/mcrf.2017016 [13] Peng Zhang, Jiequan Li, Tong Zhang. On two-dimensional Riemann problem for pressure-gradient equations of the Euler system. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 609-634. doi: 10.3934/dcds.1998.4.609 [14] Shu Wang, Chundi Liu. Boundary Layer Problem and Quasineutral Limit of Compressible Euler-Poisson System. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2177-2199. doi: 10.3934/cpaa.2017108 [15] Eugenio Aulisa, Lidia Bloshanskaya, Akif Ibragimov. Well productivity index for compressible fluids and gases. Evolution Equations & Control Theory, 2016, 5 (1) : 1-36. doi: 10.3934/eect.2016.5.1 [16] Yanbo Hu, Wancheng Sheng. The Riemann problem of conservation laws in magnetogasdynamics. Communications on Pure & Applied Analysis, 2013, 12 (2) : 755-769. doi: 10.3934/cpaa.2013.12.755 [17] Ju Ge, Wancheng Sheng. The two dimensional gas expansion problem of the Euler equations for the generalized Chaplygin gas. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2733-2748. doi: 10.3934/cpaa.2014.13.2733 [18] Rinaldo M. Colombo, Graziano Guerra. A coupling between a non--linear 1D compressible--incompressible limit and the 1D $p$--system in the non smooth case. Networks & Heterogeneous Media, 2016, 11 (2) : 313-330. doi: 10.3934/nhm.2016.11.313 [19] Van-Sang Ngo, Stefano Scrobogna. Dispersive effects of weakly compressible and fast rotating inviscid fluids. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 749-789. doi: 10.3934/dcds.2018033 [20] Konstantina Trivisa. Global existence and asymptotic analysis of solutions to a model for the dynamic combustion of compressible fluids. Conference Publications, 2003, 2003 (Special) : 852-863. doi: 10.3934/proc.2003.2003.852

2018 Impact Factor: 0.871