-
Previous Article
Existence of solutions for singularly perturbed Schrödinger equations with nonlocal part
- CPAA Home
- This Issue
-
Next Article
Long-time dynamics of the parabolic $p$-Laplacian equation
The Riemann problem of conservation laws in magnetogasdynamics
1. | Department of Mathematics, Shanghai University, Shanghai, 200444, China |
References:
[1] |
W. R. Hu, "Universe Magnetogasdynamics" (in Chinese), Science Press, Beijing, 1987. |
[2] |
D. Q. Li and T. H. Qin, "Physics and Partial Differential Equations" (in Chinese), Higher Education Press, 2005. |
[3] |
H. Cabannes, "Theoretical Magnetofluid Dynamics, in: Applid Mathematics and Mechanics," Academic Press, New York, 1970. |
[4] |
R. Gundersen, "Linearized Analysis of One-dimensional Magnetohydrodynamic Flows," Springer-Verlag, Berlin, 1964. |
[5] |
R. S. Myong and P. L. Roe, Shock waves and rarefaction waves in magnetohydrodynamics part 1. a model system, J. Plasma Phys., 58 (1997), 485-519.
doi: 10.1017/S002237789700593X. |
[6] |
R. S. Myong and P. L. Roe, Shock waves and rarefaction waves in magnetohydrodynamics part 2. the MHD system, J. Plasma Phys., 58 (1997), 521-552.
doi: 10.1017/S0022377897005941. |
[7] |
M. Torrilhon, "Exact Solver and Uniqueness Conditions for Riemann Problem of Ideal Magnetohydrodynamics," Seminar für Angewandte Mathematik Eidgenössische Technische Hochschule, Switzerland, 2002. |
[8] |
T. R. Sekhar and V. D. Sharma, Riemann problem and elementary wave interactions in isentropic magnetogasdynamics, Nonlinear Analysis: Real World Applications, 11 (2010), 619-636.
doi: 10.1016/j.nonrwa.2008.10.036. |
[9] |
R. Courant and K. O. Friedrichs, "Supersonic Flow and Shock Waves," Intersience Publisher, New York, 1999. |
[10] |
P. D. Lax, Hyperbolic system of conservation laws II, Comm. Pure Appl. Math., 10 (1957), 537-566.
doi: 10.1002/cpa.3160100406. |
[11] |
J. Glimm, Solutions in the large for nonlinear hyperbolic system of equations, Comm. Pure Appl. Math., 18 (1963), 697-715.
doi: 10.1002/cpa.3160180408. |
[12] |
T. P. Liu, Existence and uniqueness theorems for Riemann problems, Trans. Amer. Math. Soc., 212 (1975), 375-382.
doi: 10.1090/S0002-9947-1975-0380135-2. |
[13] |
T. Chang and L. Hsiao, "The Riemann Problem and Interaction of Waves in Gas Dynamics," Longman, Harlow, 1989. |
[14] |
J. Smollor, "Shock Waves and Reaction Diffusion Equations," Springer Verlag, New York, 1994. |
[15] |
Y. B. Hu and W. C. Sheng, Elementary waves of conservation laws in magnetogasdynamics (in Chinese), Commun. Appl. Math. Comput., 23 (2009), 49-54. |
show all references
References:
[1] |
W. R. Hu, "Universe Magnetogasdynamics" (in Chinese), Science Press, Beijing, 1987. |
[2] |
D. Q. Li and T. H. Qin, "Physics and Partial Differential Equations" (in Chinese), Higher Education Press, 2005. |
[3] |
H. Cabannes, "Theoretical Magnetofluid Dynamics, in: Applid Mathematics and Mechanics," Academic Press, New York, 1970. |
[4] |
R. Gundersen, "Linearized Analysis of One-dimensional Magnetohydrodynamic Flows," Springer-Verlag, Berlin, 1964. |
[5] |
R. S. Myong and P. L. Roe, Shock waves and rarefaction waves in magnetohydrodynamics part 1. a model system, J. Plasma Phys., 58 (1997), 485-519.
doi: 10.1017/S002237789700593X. |
[6] |
R. S. Myong and P. L. Roe, Shock waves and rarefaction waves in magnetohydrodynamics part 2. the MHD system, J. Plasma Phys., 58 (1997), 521-552.
doi: 10.1017/S0022377897005941. |
[7] |
M. Torrilhon, "Exact Solver and Uniqueness Conditions for Riemann Problem of Ideal Magnetohydrodynamics," Seminar für Angewandte Mathematik Eidgenössische Technische Hochschule, Switzerland, 2002. |
[8] |
T. R. Sekhar and V. D. Sharma, Riemann problem and elementary wave interactions in isentropic magnetogasdynamics, Nonlinear Analysis: Real World Applications, 11 (2010), 619-636.
doi: 10.1016/j.nonrwa.2008.10.036. |
[9] |
R. Courant and K. O. Friedrichs, "Supersonic Flow and Shock Waves," Intersience Publisher, New York, 1999. |
[10] |
P. D. Lax, Hyperbolic system of conservation laws II, Comm. Pure Appl. Math., 10 (1957), 537-566.
doi: 10.1002/cpa.3160100406. |
[11] |
J. Glimm, Solutions in the large for nonlinear hyperbolic system of equations, Comm. Pure Appl. Math., 18 (1963), 697-715.
doi: 10.1002/cpa.3160180408. |
[12] |
T. P. Liu, Existence and uniqueness theorems for Riemann problems, Trans. Amer. Math. Soc., 212 (1975), 375-382.
doi: 10.1090/S0002-9947-1975-0380135-2. |
[13] |
T. Chang and L. Hsiao, "The Riemann Problem and Interaction of Waves in Gas Dynamics," Longman, Harlow, 1989. |
[14] |
J. Smollor, "Shock Waves and Reaction Diffusion Equations," Springer Verlag, New York, 1994. |
[15] |
Y. B. Hu and W. C. Sheng, Elementary waves of conservation laws in magnetogasdynamics (in Chinese), Commun. Appl. Math. Comput., 23 (2009), 49-54. |
[1] |
Feimin Huang, Yi Wang, Tong Yang. Fluid dynamic limit to the Riemann Solutions of Euler equations: I. Superposition of rarefaction waves and contact discontinuity. Kinetic and Related Models, 2010, 3 (4) : 685-728. doi: 10.3934/krm.2010.3.685 |
[2] |
Eun Heui Kim, Charis Tsikkou. Two dimensional Riemann problems for the nonlinear wave system: Rarefaction wave interactions. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6257-6289. doi: 10.3934/dcds.2017271 |
[3] |
Feng Xie. Nonlinear stability of combination of viscous contact wave with rarefaction waves for a 1D radiation hydrodynamics model. Discrete and Continuous Dynamical Systems - B, 2012, 17 (3) : 1075-1100. doi: 10.3934/dcdsb.2012.17.1075 |
[4] |
Cristóbal Rodero, J. Alberto Conejero, Ignacio García-Fernández. Shock wave formation in compliant arteries. Evolution Equations and Control Theory, 2019, 8 (1) : 221-230. doi: 10.3934/eect.2019012 |
[5] |
Jianjun Chen, Wancheng Sheng. The Riemann problem and the limit solutions as magnetic field vanishes to magnetogasdynamics for generalized Chaplygin gas. Communications on Pure and Applied Analysis, 2018, 17 (1) : 127-142. doi: 10.3934/cpaa.2018008 |
[6] |
Renjun Duan, Xiongfeng Yang. Stability of rarefaction wave and boundary layer for outflow problem on the two-fluid Navier-Stokes-Poisson equations. Communications on Pure and Applied Analysis, 2013, 12 (2) : 985-1014. doi: 10.3934/cpaa.2013.12.985 |
[7] |
Qingqing Liu, Xiaoli Wu. Stability of rarefaction wave for viscous vasculogenesis model. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022034 |
[8] |
Lili Fan, Lizhi Ruan, Wei Xiang. Asymptotic stability of viscous contact wave for the inflow problem of the one-dimensional radiative Euler equations. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1971-1999. doi: 10.3934/dcds.2020349 |
[9] |
Teng Wang, Yi Wang. Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equation. Kinetic and Related Models, 2019, 12 (3) : 637-679. doi: 10.3934/krm.2019025 |
[10] |
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 and Continuous Dynamical Systems, 1995, 1 (4) : 555-584. doi: 10.3934/dcds.1995.1.555 |
[11] |
Haiyan Yin. The stability of contact discontinuity for compressible planar magnetohydrodynamics. Kinetic and Related Models, 2017, 10 (4) : 1235-1253. doi: 10.3934/krm.2017047 |
[12] |
Anupam Sen, T. Raja Sekhar. Delta shock wave and wave interactions in a thin film of a perfectly soluble anti-surfactant solution. Communications on Pure and Applied Analysis, 2020, 19 (5) : 2641-2653. doi: 10.3934/cpaa.2020115 |
[13] |
Tung Chang, Gui-Qiang Chen, Shuli Yang. On the 2-D Riemann problem for the compressible Euler equations II. Interaction of contact discontinuities. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 419-430. doi: 10.3934/dcds.2000.6.419 |
[14] |
Huancheng Yao, Haiyan Yin, Changjiang Zhu. Stability of rarefaction wave for the compressible non-isentropic Navier-Stokes-Maxwell equations. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1297-1317. doi: 10.3934/cpaa.2021021 |
[15] |
Li Fang, Zhenhua Guo. Zero dissipation limit to rarefaction wave with vacuum for a one-dimensional compressible non-Newtonian fluid. Communications on Pure and Applied Analysis, 2017, 16 (1) : 209-242. doi: 10.3934/cpaa.2017010 |
[16] |
Shu Wang, Yixuan Zhao. Asymptotic stability of planar rarefaction wave to a multi-dimensional two-phase flow. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022091 |
[17] |
Feimin Huang, Xiaoding Shi, Yi Wang. Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary. Kinetic and Related Models, 2010, 3 (3) : 409-425. doi: 10.3934/krm.2010.3.409 |
[18] |
Mikko Kemppainen, Peter Sjögren, José Luis Torrea. Wave extension problem for the fractional Laplacian. Discrete and Continuous Dynamical Systems, 2015, 35 (10) : 4905-4929. doi: 10.3934/dcds.2015.35.4905 |
[19] |
Zhilei Liang. Convergence rate of solutions to the contact discontinuity for the compressible Navier-Stokes equations. Communications on Pure and Applied Analysis, 2013, 12 (5) : 1907-1926. doi: 10.3934/cpaa.2013.12.1907 |
[20] |
Zhi-Qiang Shao. Lifespan of classical discontinuous solutions to the generalized nonlinear initial-boundary Riemann problem for hyperbolic conservation laws with small BV data: shocks and contact discontinuities. Communications on Pure and Applied Analysis, 2015, 14 (3) : 759-792. doi: 10.3934/cpaa.2015.14.759 |
2021 Impact Factor: 1.273
Tools
Metrics
Other articles
by authors
[Back to Top]