JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (10): 89-100.doi: 10.6040/j.issn.1671-9352.0.2023.165
YANG Fan, GUO Lihui*
CLC Number:
| [1] 王明亮,周宇斌. 变色散系数的非线性色谱方程[J]. 烟台大学学报(自然科学与工程版), 1996(1):7-13. WANG Mingliang, ZHOU Yubin. An equation of nonlinear chromatography with variable dispersion coefficient[J]. Journal of Yantai University(Natural Science and Engineering), 1996(1):7-13. [2] SUN Meina. Shadow wave solution for the generalized langmuir isotherm in chromatography[J]. Archiv der Mathematik, 2016, 107:645-658. [3] CHENG Hongjun, YANG Hanchun. Delta shock waves in chromatography equations[J]. Journal of Mathematical Analysis and Applications, 2011, 380(2):475-485. [4] WANG Guodong. One-dimensional nonlinear chromatography system and delta-shock waves[J]. Zeitschrift für Angewandte Mathematik und Physik, 2013, 64(5):1451-1469. [5] GUO Lihui, PAN Lijun, YIN Gan. The perturbed Riemann problem and delta contact discontinuity in chromatography equations[J]. Nonlinear Analysis:Theory, Methods & Applications, 2014, 106:110-123. [6] SHEN Chun. The asymptotic behaviors of solutions to the perturbed Riemann problem near the singular curve for the chromatography system[J]. Journal of Nonlinear Mathematical Physics, 2015, 22(1):76-101. [7] SUN Meina. Delta shock waves for the chromatography equations as self-similar viscosity limits[J]. Quarterly of Applied Mathematics, 2011, 69(3):425-443. [8] ZHANG Qingling. Interactions of delta shock waves and stability of Riemann solutions for nonlinear chromatography equations[J]. Zeitschrift für angewandte Mathematik und Physik, 2016, 67:15. [9] SUN Meina. Interactions of delta shock waves for the chromatography equations[J]. Applied Mathematics Letters, 2013, 26(6):631-637. [10] WEI Zhijian, SUN Meina. Exact delta shock wave solution to the Riemann problem for the three-component chromatography model[J]. Computational and Applied Mathematics, 2022, 41(4):133. [11] MAZZOTTI M, TARAFDER A, CORNEL J, et al. Experimental evidence of a delta-shock in nonlinear chromatography[J]. Journal of Chromatography A, 2010, 1217(13):2002-2012. [12] NEDELJKOV M. Shadow waves:entropies and interactions for delta and singular shocks[J]. Archive for Rational Mechanics and analysis, 2010, 197(2):489-537. [13] NEDELJKOV M. Higher order shadow waves and delta shock blow up in the Chaplygin gas[J]. Journal of Differential Equations, 2014, 256(11):3859-3887. [14] NEDELJKOV M, NEUMANN L, OBERGUGGENBERGER M, et al. Radially symmetric shadow wave solutions to the system of pressureless gas dynamics in arbitrary dimensions[J]. Nonlinear Analysis, 2017, 163:104-126. [15] 贾艺菲, 郭俐辉, 白寅松. 相对论Chaplygin气体欧拉方程组的阴影波解[J]. 山东大学学报(理学版), 2022, 57(4):55-65. JIA Yifei, GUO Lihui, BAI Yinsong. Shadow wave solution for the relativistic Chaplygin Euler equations[J]. Journal of Shandong University(Natural Science), 2022, 57(4):55-65. [16] DAW D A E, NEDELJKOV M. Shadow waves for pressureless gas balance laws[J]. Applied Mathematics Letters, 2016, 57:54-59. [17] KRUNIC T, NEDELJKOV M. Shadow wave solutions for a scalar two-flux conservation law with Rankine-Hugoniot deficit[J]. Journal of Hyperbolic Differential Equations, 2021, 18(3):539-556. [18] RUŽICIC S, NEDELJKOV M. Shadow wave tracking procedure and initial data problem for pressureless gas model[J]. Acta Applicandae Mathematicae, 2021, 171:1-36. [19] KORCHINSKI D J. Solution of a riemann problem for a 2×2 system of conservation laws possessing no classical weak solution[D]. Garden City: Adelphi University, 1977. [20] WANG Zhen, ZHANG Qingling. The Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations[J]. Acta Mathematica Scientia, 2012, 32(3):825-841. [21] CHENG Hongjun, YANG Hanchun. Riemann problem for the relativistic Chaplygin Euler equations[J]. Journal of Mathema-tical Analysis and Applications, 2011, 381(1):17-26. [22] NEDELJKOV M, OBERGUGGENBERGER M. Interactions of delta shock waves in a strictly hyperbolic system of conservation laws[J]. Journal of Mathematical Analysis and Applications, 2008, 344(2):1143-1157. [23] TAN Dechun, ZHANG Tong, CHANG Tung, et al. Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws[J]. Journal of Differential Equations, 1994, 112(1):1-32. [24] DANILOV V, SHELKOVICH V. Delta-shock wave type solution of hyperbolic systems of conservation laws[J]. Quarterly of Applied Mathematics, 2005, 63(3):401-427. [25] SARRICO C O R, PAIVA A. Delta shock waves in the shallow water system[J]. Journal of Dynamics and Differential Equations, 2018, 30:1187-1198. [26] ABREU E, LAMBERT W. Riemann problems and delta-shock solutions for a Keyfitz-Kranzer system with a forcing term[J]. Journal of Mathematical Analysis and Applications, 2021, 502(2):125267. [27] PANG Yicheng. Delta shock wave in the compressible Euler equations for a Chaplygin gas[J]. Journal of Mathematical Analysis and Applications, 2017, 448(1):245-261. [28] 俞康宁, 郭俐辉. 带有源项的广义Chaplygin气体磁流体Euler方程组Riemann解的极限[J]. 应用数学与力学, 2020, 41(4):420-437. YU Kangning, GUO Lihui. Limits of Riemann solutions for generalized Chaplygin gas magnetohydrodynamic Euler equations with source terms[J]. Applied Mathematics & Mechanics, 2020, 41(4):420-437. [29] LIU Dongdong, YU Kangning, GUO Lihui. The initial-boundary value problem for a strictly hyperbolic equations[J]. Computational and Applied Mathematics, 2022, 41(5):197. [30] TEMPLE B. Systems of conservation laws with invariant submanifolds[J]. Transactions of the American Mathematical Society, 1983, 280(2):781-795. [31] TEMPLE B. Global solution of the Cauchy problem for a class of 2× 2 nonstrictly hyperbolic conservation laws[J]. Advances in Applied Mathematics, 1982, 3(3):335-375. |
| [1] | JIA Yi-fei, GUO Li-hui, BAI Yin-song. Shadow wave solution for the relativistic Chaplygin Euler equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(4): 55-65. |
|
||
