Tian, Yuan; Shen, Chun Delta shock formation for the isothermal and logarithmic-corrected Chaplygin Euler equations. (English) Zbl 1526.35235 Bull. Malays. Math. Sci. Soc. (2) 46, No. 6, Paper No. 192, 34 p. (2023). MSC: 35L67 35L65 35Q31 76N15 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{C. Shen}, Bull. Malays. Math. Sci. Soc. (2) 46, No. 6, Paper No. 192, 34 p. (2023; Zbl 1526.35235) Full Text: DOI
Liu, Xiaolin; Shen, Chun Stability of delta shock solution for the simplified magnetohydrodynamics equations under the linear flux-function perturbation. (English) Zbl 1504.35190 Acta Appl. Math. 183, Paper No. 1, 28 p. (2023). MSC: 35L65 35L67 76N15 76W05 PDFBibTeX XMLCite \textit{X. Liu} and \textit{C. Shen}, Acta Appl. Math. 183, Paper No. 1, 28 p. (2023; Zbl 1504.35190) Full Text: DOI
Shan, Shan; Shen, Chun; Wei, Zhijian The adiabatic exponent limits of Riemann solutions for the extended macroscopic production model. (English) Zbl 1514.35284 Math. Model. Nat. Phenom. 17, Paper No. 26, 23 p. (2022). MSC: 35L67 35L45 35L65 76N15 PDFBibTeX XMLCite \textit{S. Shan} et al., Math. Model. Nat. Phenom. 17, Paper No. 26, 23 p. (2022; Zbl 1514.35284) Full Text: DOI
Li, Shuangrong; Shen, Chun On the wave interactions for the drift-flux equations with the Chaplygin gas. (English) Zbl 1491.35289 Monatsh. Math. 197, No. 4, 635-654 (2022). Reviewer: Vincent Duchêne (Rennes) MSC: 35L67 35L45 35L60 35L65 76N15 PDFBibTeX XMLCite \textit{S. Li} and \textit{C. Shen}, Monatsh. Math. 197, No. 4, 635--654 (2022; Zbl 1491.35289) Full Text: DOI
Shen, Chun; Sun, Meina Formation of vacuum state and delta shock wave for the relativistic Euler system for polytropic gas with the varying \(\gamma\)-law. (English) Zbl 1490.35284 Z. Angew. Math. Phys. 73, No. 2, Paper No. 69, 28 p. (2022). MSC: 35Q31 35L65 35L67 76N15 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, Z. Angew. Math. Phys. 73, No. 2, Paper No. 69, 28 p. (2022; Zbl 1490.35284) Full Text: DOI
Shen, Chun; Sun, Meina Exact Riemann solutions for the drift-flux equations of two-phase flow under gravity. (English) Zbl 1508.35091 J. Differ. Equations 314, 1-55 (2022). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q35 76T10 76L05 76P05 76N15 35L65 35L67 35B40 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, J. Differ. Equations 314, 1--55 (2022; Zbl 1508.35091) Full Text: DOI
Shen, Chun; Sun, Meina The multiplication of distributions in the study of delta shock wave for a hyperbolic system of temple class. (English) Zbl 1485.35292 Int. J. Math. 32, No. 14, Article ID 2150103, 20 p. (2021). MSC: 35L65 35L67 46F10 76N15 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, Int. J. Math. 32, No. 14, Article ID 2150103, 20 p. (2021; Zbl 1485.35292) Full Text: DOI
Wang, Pengyan; Shen, Chun The perturbed Riemann problem for a macroscopic production model with Chaplygin gas. (English) Zbl 1465.35305 Bull. Malays. Math. Sci. Soc. (2) 44, No. 3, 1195-1214 (2021). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 35L67 35L65 76N15 35Q31 PDFBibTeX XMLCite \textit{P. Wang} and \textit{C. Shen}, Bull. Malays. Math. Sci. Soc. (2) 44, No. 3, 1195--1214 (2021; Zbl 1465.35305) Full Text: DOI
Shen, Chun The asymptotic limits of Riemann solutions for the isentropic drift-flux model of compressible two-phase flows. (English) Zbl 1452.35102 Math. Methods Appl. Sci. 43, No. 6, 3673-3688 (2020). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 35L67 35L65 76N15 76T10 35Q31 PDFBibTeX XMLCite \textit{C. Shen}, Math. Methods Appl. Sci. 43, No. 6, 3673--3688 (2020; Zbl 1452.35102) Full Text: DOI
Shen, Chun; Sun, Meina The singular limits of Riemann solutions to a chemotaxis model with flux perturbation. (English) Zbl 07785930 ZAMM, Z. Angew. Math. Mech. 99, No. 7, Article ID e201800046, 28 p. (2019). MSC: 35L65 35L67 35B25 90B20 92C17 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, ZAMM, Z. Angew. Math. Mech. 99, No. 7, Article ID e201800046, 28 p. (2019; Zbl 07785930) Full Text: DOI
Tong, Meizi; Shen, Chun The limits of Riemann solutions for the isentropic Euler system with extended Chaplygin gas. (English) Zbl 1426.35160 Appl. Anal. 98, No. 15, 2668-2687 (2019). MSC: 35L67 35L65 76N15 35Q31 PDFBibTeX XMLCite \textit{M. Tong} and \textit{C. Shen}, Appl. Anal. 98, No. 15, 2668--2687 (2019; Zbl 1426.35160) Full Text: DOI
Wang, Pengyan; Shen, Chun; Lin, Xiuli Construction of global solutions for a symmetric system of Keyfitz-Kranzer type with three piecewise constant states. (English) Zbl 1458.35266 Adv. Difference Equ. 2019, Paper No. 69, 18 p. (2019). MSC: 35L65 35L67 PDFBibTeX XMLCite \textit{P. Wang} et al., Adv. Difference Equ. 2019, Paper No. 69, 18 p. (2019; Zbl 1458.35266) Full Text: DOI
Tong, Meizi; Shen, Chun; Lin, Xiuli The asymptotic limits of Riemann solutions for the isentropic extended Chaplygin gas dynamic system with the vanishing pressure. (English) Zbl 1499.35405 Bound. Value Probl. 2018, Paper No. 144, 20 p. (2018). MSC: 35L65 35L67 76N15 PDFBibTeX XMLCite \textit{M. Tong} et al., Bound. Value Probl. 2018, Paper No. 144, 20 p. (2018; Zbl 1499.35405) Full Text: DOI
Shen, Chun; Sheng, Wancheng; Sun, Meina The asymptotic limits of solutions to the Riemann problem for the scaled leroux system. (English) Zbl 1387.35410 Commun. Pure Appl. Anal. 17, No. 2, 391-411 (2018). MSC: 35L65 35L67 35B25 PDFBibTeX XMLCite \textit{C. Shen} et al., Commun. Pure Appl. Anal. 17, No. 2, 391--411 (2018; Zbl 1387.35410) Full Text: DOI
Shen, Chun Delta shock wave solution for a symmetric Keyfitz-Kranzer system. (English) Zbl 1380.35126 Appl. Math. Lett. 77, 35-43 (2018). MSC: 35L67 35L65 35L45 PDFBibTeX XMLCite \textit{C. Shen}, Appl. Math. Lett. 77, 35--43 (2018; Zbl 1380.35126) Full Text: DOI
Jiang, Yuhao; Shen, Chun The perturbed Riemann problem for special Keyfitz-Kranzer system with three piecewise constant states. (English) Zbl 1400.35180 Adv. Math. Phys. 2017, Article ID 3276182, 12 p. (2017). MSC: 35L67 35L65 35L45 PDFBibTeX XMLCite \textit{Y. Jiang} and \textit{C. Shen}, Adv. Math. Phys. 2017, Article ID 3276182, 12 p. (2017; Zbl 1400.35180) Full Text: DOI
Shen, Chun The Riemann problem for the Chaplygin gas equations with a source term. (English) Zbl 07775057 ZAMM, Z. Angew. Math. Mech. 96, No. 6, 681-695 (2016). MSC: 35L67 35L65 35B30 76N10 PDFBibTeX XMLCite \textit{C. Shen}, ZAMM, Z. Angew. Math. Mech. 96, No. 6, 681--695 (2016; Zbl 07775057) Full Text: DOI
Ji, Pengpeng; Shen, Chun The perturbed Riemann problem for the chromatography system of Langmuir isotherm with one inert component. (English) Zbl 1378.35197 J. Nonlinear Sci. Appl. 9, No. 9, 5382-5397 (2016). MSC: 35L67 35L65 76N15 PDFBibTeX XMLCite \textit{P. Ji} and \textit{C. Shen}, J. Nonlinear Sci. Appl. 9, No. 9, 5382--5397 (2016; Zbl 1378.35197) Full Text: DOI Link
Wei, Xuefeng; Shen, Chun Structural stability of Riemann solutions for strictly hyperbolic systems with three piecewise constant states. (English) Zbl 1353.35204 Electron. J. Differ. Equ. 2016, Paper No. 320, 25 p. (2016). MSC: 35L65 35L67 76N15 PDFBibTeX XMLCite \textit{X. Wei} and \textit{C. Shen}, Electron. J. Differ. Equ. 2016, Paper No. 320, 25 p. (2016; Zbl 1353.35204) Full Text: Link
Shen, Chun The Riemann problem for the pressureless Euler system with the Coulomb-like friction term. (English) Zbl 1336.35281 IMA J. Appl. Math. 81, No. 1, 76-99 (2016). MSC: 35Q31 76L05 35L65 PDFBibTeX XMLCite \textit{C. Shen}, IMA J. Appl. Math. 81, No. 1, 76--99 (2016; Zbl 1336.35281) Full Text: DOI
Zhang, Ting; Shen, Chun The shock wave solution to the Riemann problem for the Burgers equation with the linear forcing term. (English) Zbl 1335.35158 Appl. Anal. 95, No. 2, 283-302 (2016). MSC: 35L67 35L65 35B25 90B20 PDFBibTeX XMLCite \textit{T. Zhang} and \textit{C. Shen}, Appl. Anal. 95, No. 2, 283--302 (2016; Zbl 1335.35158) Full Text: DOI
Yin, Gan; Shen, Chun; Guo, Lihui WITHDRAWN: The Vanishing Pressure Limits of Riemann Solutions to the Chaplygin Euler Equations. arXiv:1605.04483 Preprint, arXiv:1605.04483 [math.AP] (2016); retraction notice ibid. MSC: 35L65 35L67 76N15 BibTeX Cite \textit{G. Yin} et al., ``WITHDRAWN: The Vanishing Pressure Limits of Riemann Solutions to the Chaplygin Euler Equations'', Preprint, arXiv:1605.04483 [math.AP] (2016); retraction notice ibid. Full Text: arXiv OA License
Shen, Chun The asymptotic behaviors of solutions to the perturbed Riemann problem near the singular curve for the chromatography system. (English) Zbl 1420.35160 J. Nonlinear Math. Phys. 22, No. 1, 76-101 (2015). MSC: 35L65 35L67 76N15 PDFBibTeX XMLCite \textit{C. Shen}, J. Nonlinear Math. Phys. 22, No. 1, 76--101 (2015; Zbl 1420.35160) Full Text: DOI
Li, Xiumei; Shen, Chun The delta standing wave solution for the linear scalar conservation law with discontinuous coefficients using a self-similar viscous regularization. (English) Zbl 1336.35234 Bull. Korean Math. Soc. 52, No. 6, 1945-1962 (2015). MSC: 35L65 35L67 76N15 35R05 35B25 PDFBibTeX XMLCite \textit{X. Li} and \textit{C. Shen}, Bull. Korean Math. Soc. 52, No. 6, 1945--1962 (2015; Zbl 1336.35234) Full Text: DOI
Shen, Chun Riemann problem for a two-dimensional quasilinear hyperbolic system. (English) Zbl 1336.35240 Electron. J. Differ. Equ. 2015, Paper No. 237, 13 p. (2015). MSC: 35L67 35L65 76N15 35L45 PDFBibTeX XMLCite \textit{C. Shen}, Electron. J. Differ. Equ. 2015, Paper No. 237, 13 p. (2015; Zbl 1336.35240) Full Text: EMIS
Shen, Chun; Sun, Meina Instability of Riemann solutions to a scalar conservation law with discontinuous flux. (English) Zbl 1320.35212 Z. Angew. Math. Phys. 66, No. 3, 499-515 (2015). MSC: 35L65 35L67 35B30 76N10 35A35 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, Z. Angew. Math. Phys. 66, No. 3, 499--515 (2015; Zbl 1320.35212) Full Text: DOI
Zhang, Ting; Shen, Chun Regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation. (English) Zbl 1470.35234 Abstr. Appl. Anal. 2014, Article ID 178672, 10 p. (2014). MSC: 35L65 35B65 35L67 35Q75 PDFBibTeX XMLCite \textit{T. Zhang} and \textit{C. Shen}, Abstr. Appl. Anal. 2014, Article ID 178672, 10 p. (2014; Zbl 1470.35234) Full Text: DOI
Lai, Geng; Shen, Chun Characteristic decompositions and boundary value problems for two-dimensional steady relativistic Euler equations. (English) Zbl 1292.35218 Math. Methods Appl. Sci. 37, No. 1, 136-147 (2014). MSC: 35Q31 35L65 35J70 35R35 35J65 PDFBibTeX XMLCite \textit{G. Lai} and \textit{C. Shen}, Math. Methods Appl. Sci. 37, No. 1, 136--147 (2014; Zbl 1292.35218) Full Text: DOI
Shen, Chun; Sun, Meina The perturbation on initial binding energy for a Majda-CJ combustion model. (English) Zbl 1273.35187 Appl. Anal. 92, No. 10, 2115-2126 (2013). MSC: 35L67 35L65 76N15 80A25 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, Appl. Anal. 92, No. 10, 2115--2126 (2013; Zbl 1273.35187) Full Text: DOI
Shen, Chun; Sun, Meina Wave interactions and stability of the Riemann solutions for a scalar conservation law with a discontinuous flux function. (English) Zbl 1272.35151 Z. Angew. Math. Phys. 64, No. 4, 1025-1056 (2013). MSC: 35L65 35L67 35B30 76N10 35B40 35C07 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, Z. Angew. Math. Phys. 64, No. 4, 1025--1056 (2013; Zbl 1272.35151) Full Text: DOI
Shen, Chun; Sun, Meina The bifurcation phenomenon for scalar conservation laws with discontinuous flux functions. (English) Zbl 1257.35128 Acta Appl. Math. 121, No. 1, 69-80 (2012). MSC: 35L67 35L65 35B30 76N10 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, Acta Appl. Math. 121, No. 1, 69--80 (2012; Zbl 1257.35128) Full Text: DOI
Shen, Chun; Sun, Meina; Wang, Zhen Global structure of Riemann solutions to a system of two-dimensional hyperbolic conservation laws. (English) Zbl 1221.35236 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 14, 4754-4770 (2011). MSC: 35L67 35L65 76N15 PDFBibTeX XMLCite \textit{C. Shen} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 14, 4754--4770 (2011; Zbl 1221.35236) Full Text: DOI
Shen, Chun The limits of Riemann solutions to the isentropic magnetogasdynamics. (English) Zbl 1215.35105 Appl. Math. Lett. 24, No. 7, 1124-1129 (2011). MSC: 35L67 35L65 76W05 PDFBibTeX XMLCite \textit{C. Shen}, Appl. Math. Lett. 24, No. 7, 1124--1129 (2011; Zbl 1215.35105) Full Text: DOI
Shen, Chun; Sun, Meina Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model. (English) Zbl 1211.35193 J. Differ. Equations 249, No. 12, 3024-3051 (2010). Reviewer: Chen Shuxing (Shanghai) MSC: 35L65 35L67 35B25 90B20 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, J. Differ. Equations 249, No. 12, 3024--3051 (2010; Zbl 1211.35193) Full Text: DOI
Shen, Chun; Sun, Meina Stability of the Riemann solutions for a nonstrictly hyperbolic system of conservation laws. (English) Zbl 1207.35057 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 10, 3284-3294 (2010). Reviewer: Shun-Tang Wu (Zhonghe) MSC: 35B35 35L65 35L67 35B30 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 10, 3284--3294 (2010; Zbl 1207.35057) Full Text: DOI
Shen, Chun; Sun, Meina; Wang, Zhen Limit relations for three simple hyperbolic systems of conservation laws. (English) Zbl 1196.35141 Math. Methods Appl. Sci. 33, No. 11, 1317-1330 (2010). MSC: 35L67 35L65 35B30 35Q31 76W05 PDFBibTeX XMLCite \textit{C. Shen} et al., Math. Methods Appl. Sci. 33, No. 11, 1317--1330 (2010; Zbl 1196.35141) Full Text: DOI
Shen, Chun Wave interactions and stability of the Riemann solutions for the chromatography equations. (English) Zbl 1184.35207 J. Math. Anal. Appl. 365, No. 2, 609-618 (2010). MSC: 35L67 35L65 35B35 PDFBibTeX XMLCite \textit{C. Shen}, J. Math. Anal. Appl. 365, No. 2, 609--618 (2010; Zbl 1184.35207) Full Text: DOI
Shen, Chun; Sun, Meina The Riemann problem for the pressure-gradient system in three pieces. (English) Zbl 1173.35595 Appl. Math. Lett. 22, No. 4, 453-458 (2009). MSC: 35L67 35L65 PDFBibTeX XMLCite \textit{C. Shen} and \textit{M. Sun}, Appl. Math. Lett. 22, No. 4, 453--458 (2009; Zbl 1173.35595) Full Text: DOI
Sun, Meina; Shen, Chun On the Riemann problem for 2D compressible Euler equations in three pieces. (English) Zbl 1169.35359 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 11, 3773-3780 (2009). MSC: 35L65 35L67 76N15 PDFBibTeX XMLCite \textit{M. Sun} and \textit{C. Shen}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 11, 3773--3780 (2009; Zbl 1169.35359) Full Text: DOI