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| 1 | Delta Shocks and Vacuum States in Vanishing Pressure Limits of Solutions to the Relativistic Euler Equations显示文摘The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity. | Gan YIN Wancheng SHENG | 2008 | Chinese Annals of Mathematics,Series B2008，29，6： | 4 |
| 2 | The Non-selfsimilar Riemann Problem for 2-D Zero-Pressure Flow in Gas Dynamics显示文摘为在有一条凸的曲线分开的二个经常的状态的煤气的动力学的二维的零压力的流动的 non-selfsimilar Riemann 问题被考虑。借助于概括 Rankine-Hugoniot 关系;概括典型分析方法,包含三角洲冲击波的全球答案;真空被构造。一种特殊情况的明确的解决方案也被给。 | Wenhua SUN Wancheng SHENG | 2007 | Chinese Annals of Mathematics,Series B2007，28，6： | 4 |
| 3 | Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow显示文摘The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied.The solutions are constructed globally under the generalized Rankine-Hugoniot relations,the δ-entropy conditions,and the generalized δ-entropy conditions.A new Delta wave,which is called a primary Delta wave,is defined in some solutions.The primary Delta wave satisfies the generalized RankineHugoniot relations and the generalized δ-entropy conditions.It generates initially from the Delta initial data,which either evaluates a Delta wave,whose weight becomes stronger and stronger,or disappears at a finite time. | Wancheng SHENG Ying ZENG | 2015 | Applied Mathematics and Mechanics(English Edition)2015，36，3： | 1 |
| 4 | The Riemann Problem for a Blood Flow Model in Arteries显示文摘In this paper,the Riemann solutions of a reduced 6×6 blood flow model in mediumsized to large vessels are constructed.The model is nonstrictly hyperbolic and non-conservative in nature,which brings two difficulties of the Riemann problem.One is the appearance of resonance while the other one is loss of uniqueness.The elementary waves include shock wave,rarefaction wave,contact discontinuity and stationary wave.The stationary wave is obtained by solving a steady equation.We construct the Riemann solutions especially when the steady equation has no solution for supersonic initial data.We also verify that the global entropy condition proposed by C.Dafermos can be used here to select the physical relevant solution.The Riemann solutions may contribute to the design of numerical schemes,which can apply to the complex blood flows. | Wancheng Sheng Qinglong Zhang Yuxi Zheng | 2020 | Communications in Computational Physics2020，27，1： | 1 |
| 5 | The two-dimensional Riemann problem for isentropic Chaplygin gas dynamicsystem显示文摘 | Guo Lihui Sheng Wancheng Zhang Tong | 2010 | Communications on Pure and Applied Analysis2010，2，9： | 1 |
| 6 | Two-Dimensional Riemann Problem for Scalar Conservation Laws显示文摘 | Sheng Wancheng | 2002 | J Differential Equations2002，183，： | 1 |
| 7 | THE GENERALIZED RIEMANN PROBLEM FOR A SCALAR COMBUSTION MODEL --THE PERTURBATION ON INITIAL BINDING ENERGY显示文摘 | Pan Lijun Sheng Wancheng | 2008 | Journal of Partial Differential Equations2008，21，4： | 1 |
| 8 | The Expansion of a Wedge of Gas into Vacuum with Small Angle in Two-Dimensional Isothermal Flow显示文摘In this paper, the authors consider the expansion problem of a wedge of gas into vacuum for the two-dimensional Euler equations in isothermal flow. By the bootstrapping argument, they prove the global existence of the smooth solution through the direct method in the case 0 < θ≤ = arctan1/(2^(1/2)+5^(1/2)), where θ is the half angle of the wedge. Furthermore,they get the uniform C^(1,1) estimates of the solution to the expansion problem. | Ju GE Wancheng SHENG | 2016 | Chinese Annals of Mathematics,Series B2016，37，3： | 0 |
| 9 | The Riemann Problem for Chaplygin Gas Flow in a Duct with Discontinuous Cross-Section显示文摘The fluid flows in a variable cross-section duct are nonconservative because of the source term.Recently,the Riemann problem and the interactions of the elementary waves for the compressible isentropic gas in a variable cross-section duct were studied.In this paper,the Riemann problem for Chaplygin gas flow in a duct with discontinuous cross-section is studied.The elementary waves include rarefaction waves,shock waves,delta waves and stationary waves. | Liancheng DANG Wancheng SHENG | 2020 | Chinese Annals of Mathematics,Series B2020，41，4： | 0 |
| 10 | Preface to the Focused Issue in Honor of Professor Tong Zhang on the Occasion of His 90th Birthday显示文摘December 9,2022 is the 90th birthday of Tong Zhang,a mathematician in Institute of Mathematics,Chinese Academy of Sciences where he was always working on the Riemann problem for gas dynamics in his mathematical life.To celebrate his 90th birthday and great contributions to this specifc feld,we organize this focused issue in the journal Communications on Applied Mathematics and Computation,since the Riemann problem has been proven to be a building block in all felds of theory,numerics and applications of hyperbolic conservation laws. | Jiequan Li Wancheng Sheng Chi-Wang Shu Ping Zhang Yuxi Zheng | 2023 | Communications on Applied Mathematics and Computation2023，5，3： | 0 |
| 11 | CAUCHY PROBLEM FOR LINEARIZED SYSTEM OF TWO-DIMENSIONAL ISENTROPIC FLOW WITH AXISYMMETRICAL INITIAL DATA IN GAS DYNAMICS显示文摘. The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given. | Zhang Hua Sheng Wancheng | 2006 | Applied Mathematics(A Journal of Chinese Universities)2006，21，1： | 0 |
| 12 | Centered simple waves for the two-dimensional pseudo-steady isothermal ?ow around a convex corner显示文摘The two-dimensional(2D) pseudo-steady isothermal flow, which is isentropic and irrotational, around a convex corner is studied. The self-similar solutions for the supersonic flow around the convex corner are constructed, where the properties of the centered simple wave are used for the 2D isentropic irrotational pseudo-steady Euler equations. The geometric procedures of the center simple waves are given. It is proven that the supersonic flow turns the convex corner by an incomplete centered expansion wave or an incomplete centered compression wave, depending on the conditions of the downstream state. | Wancheng SHENG Aidi YAO | 2019 | Applied Mathematics and Mechanics(English Edition)2019，40，5： | 0 |
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