Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (4): 1519-1535.doi: 10.1007/s10473-022-0413-4
• Articles • Previous Articles Next Articles
Sijie LIU, Wancheng SHENG
Received:
2021-02-02
Online:
2022-08-25
Published:
2022-08-23
Contact:
Wancheng SHENG,E-mail:mathwcsheng@shu.edu.cn
E-mail:mathwcsheng@shu.edu.cn
Supported by:
CLC Number:
Sijie LIU, Wancheng SHENG. THE STABILITY OF THE DELTA WAVE TO PRESSURELESS EULER EQUATIONS WITH VISCOUS AND FLUX PERTURBATIONS[J].Acta mathematica scientia,Series B, 2022, 42(4): 1519-1535.
[1] Bouchut F. On zero-pressure gas dynamics. advances in kinetic theory and computing. Ser Adv Math Appl Sci, 1994, 22:171-190 [2] Chang T, Hsiao L. The Riemann Problem and Interaction of Waves in Gas Dynamics. Essex:Longman Scientific and Technical, 1989 [3] Chen G Q, Liu H L. Formation of δ-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids. Siam J Math Anal, 2003, 34(4):925-938 [4] Chen G Q, Liu H L. Concentration and cavitaion in the vaninshing pressure limit of solutions to the Euler equations for nonisentropic fluids. Phys D, 2004, 189(1):141-165 [5] Dafermos C M. Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by viscosity method. Arch Rational Mech Anal, 1973, 52(1):1-9 [6] Dafermos C M, Diperna R J. The Riemann problem for certain classes of hyperbolic systems of conservation laws. J Differential Equations, 1976, 20(1):90-114 [7] Hu J. The Riemann Problem for Pressureless Fluid Dynamics with Distribution Solutions in Colombeau's Sence. Comm Math Phys, 1998, 194(1):191-205 [8] Li J. Note on the Compressible Euler Equations with Zero Temperature. Appl Math Lett, 2001, 14(4):519-523 [9] Sheng W, Zhang T. The Riemann problem for the transportation eqautions in gas dynamics. Mem Amer Math Soc, 1999, 137(654):viii+77pp [10] Slemrod M, Tzavaras A E. A limiting viscosity approach for the Riemann problem in isentropic gas dynamics. Indiana Univ Math J, 1989, 38(4):1047-1074 [11] Tan D, Zhang T, Zheng Y. Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws. J Differential Equations, 1994, 112(1):1-32 [12] Yang H. Riemann problems for a class of coupled hyperbolic systems of conservation laws. J Differential Equations, 1999, 159(2):447-484 [13] Yang H. Generalized plane delta shock waves for n-dimensional zero-pressure gas dynamics. J Math Anal Appl, 2001, 260(1):18-35 [14] Yang H, Liu J. Delta-shocks and vacuums in zero-pressure gas dynamics by the flux approximation. Sci China Math, 2015, 58(11):2329-2346 [15] Yang H, Zhang Y. New developments of delta-shock waves and its applications in systems of conservation laws. J Differetial Equations, 2012, 252(11):5951-5993 [16] Yang H, Zhang Y. Delta shock waves with Dirac delta function in both Components for systems of conservation laws. J Differetial Equations, 2014, 257(12):4369-4402 [17] Zhang Y, Yang J. Vanishing viscosity limit for Riemann solutions to zero-pressure gas dynamics with flux perturbation. Boundary Value Problems, 2018, 107(1):1-27 |
[1] | Ben DUAN, Ao LAN, Zhen LUO. TRANSONIC SHOCK SOLUTIONS TO THE EULER SYSTEM IN DIVERGENT-CONVERGENT NOZZLES [J]. Acta mathematica scientia,Series B, 2022, 42(4): 1536-1546. |
[2] | Fei WU, Zejun WANG. EXISTENCE OF PERIODIC SOLUTIONS TO AN ISOTHERMAL RELATIVISTIC EULER SYSTEM [J]. Acta mathematica scientia,Series B, 2022, 42(1): 155-171. |
[3] | Yifan SU, Zhenhua GUO. ZERO DISSIPATION LIMIT TO RAREFACTION WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SELECTED DENSITY-DEPENDENT VISCOSITY [J]. Acta mathematica scientia,Series B, 2021, 41(5): 1635-1658. |
[4] | Li WANG. THE VON NEUMANN PARADOX FOR THE EULER EQUATIONS [J]. Acta mathematica scientia,Series B, 2021, 41(3): 753-763. |
[5] | MINHAJUL, T RAJA SEKHAR. NONLINEAR WAVE INTERACTIONS IN A MACROSCOPIC PRODUCTION MODEL [J]. Acta mathematica scientia,Series B, 2021, 41(3): 764-780. |
[6] | Tingting CHEN, Aifang QU, Zhen WANG. EXISTENCE AND UNIQUENESS OF THE GLOBAL L1 SOLUTION OF THE EULER EQUATIONS FOR CHAPLYGIN GAS [J]. Acta mathematica scientia,Series B, 2021, 41(3): 941-958. |
[7] | Jianwei DONG, Manwai YUEN. SOME SPECIAL SELF-SIMILAR SOLUTIONS FOR A MODEL OF INVISCID LIQUID-GAS TWO-PHASE FLOW [J]. Acta mathematica scientia,Series B, 2021, 41(1): 114-126. |
[8] | Juan C. JUAJIBIOY. ON THE CAUCHY PROBLEM FOR AW-RASCLE SYSTEM WITH LINEAR DAMPING [J]. Acta mathematica scientia,Series B, 2021, 41(1): 311-318. |
[9] | Hakho HONG. THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM [J]. Acta mathematica scientia,Series B, 2021, 41(1): 319-336. |
[10] | Weifeng JIANG, Zhen WANG. THE EXISTENCE OF A BOUNDED INVARIANT REGION FOR COMPRESSIBLE EULER EQUATIONS IN DIFFERENT GAS STATES [J]. Acta mathematica scientia,Series B, 2020, 40(5): 1229-1239. |
[11] | Jianli LIU, Jie XUE. GLOBAL SIMPLE WAVE SOLUTIONS TO A KIND OF TWO DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS [J]. Acta mathematica scientia,Series B, 2020, 40(1): 261-271. |
[12] | Chunlong YANG, Gaowei CAO, Xiaozhou YANG. UNIFORM FORMULA FOR THE RIEMANN SOLUTIONS OF A SCALAR COMBUSTION MODEL [J]. Acta mathematica scientia,Series B, 2016, 36(5): 1405-1418. |
[13] | Wentao CAO, Feimin HUANG, Tianhong LI, Huimin YU. GLOBAL ENTROPY SOLUTIONS TO AN INHOMOGENEOUS ISENTROPIC COMPRESSIBLE EULER SYSTEM [J]. Acta mathematica scientia,Series B, 2016, 36(4): 1215-1224. |
[14] | Fa WU, Huihui DAI, Dexing KONG. MECHANISM FOR THE TRANSITION FROM A REGULAR REFLECTION TO A MACH REFLECTION OR A VON NEUMANN REFLECTION [J]. Acta mathematica scientia,Series B, 2016, 36(3): 931-944. |
[15] | Hakho HONG. ZERO DISSIPATION LIMIT TO CONTACT DISCONTINUITY FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS [J]. Acta mathematica scientia,Series B, 2016, 36(1): 157-172. |
Viewed | ||||||||||||||||||||||||||||||||||||||||||||||
Full text 5
|
|
|||||||||||||||||||||||||||||||||||||||||||||
Abstract 85
|
|
|||||||||||||||||||||||||||||||||||||||||||||
Cited |
|
|||||||||||||||||||||||||||||||||||||||||||||
Shared | ||||||||||||||||||||||||||||||||||||||||||||||
Discussed |
|