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Communications in Partial Differential Equations Volume 22, 1997 - Issue 11-12
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Original Articles

Existence of solutions to the transonic pressure gradient equations of the compressible euler equations in elliptic Regions

Zheng Yuxi Department of Mathematics, Indiana University, Bloomington, IN 47405 E-mail: [email protected]
Pages 1849-1868 | Published online: 14 May 2007

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Kyungwoo Song. (2003) The Pressure-Gradient System on Non-smooth Domains. Communications in Partial Differential Equations 28:1-2, pages 199-221.
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Articles from other publishers (25)

Gui-Qiang G. Chen. (2022) Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems. Communications on Applied Mathematics and Computation 5:3, pages 1015-1052.
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Hongjun Cheng & Hanchun Yang. (2022) Riemann problems for a hyperbolic system of nonlinear conservation laws from the Liou–Steffen pressure system. Journal of Hyperbolic Differential Equations 19:03, pages 467-522.
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Hongjun Cheng & Hanchun Yang. (2021) On a Two-Dimensional Riemann Problem for Hyperbolic System of Nonlinear Conservation Laws. Acta Applicandae Mathematicae 175:1.
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Qin Wang & Kyungwoo Song. (2021) Shock Diffraction Problem by Convex Cornered Wedges for Isothermal Gas. Acta Mathematica Scientia 41:4, pages 1130-1140.
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Gui-Qiang G. Chen, Qin Wang & Shengguo Zhu. (2021) Global solutions of a two-dimensional Riemann problem for the pressure gradient system. Communications on Pure & Applied Analysis 20:7-8, pages 2475.
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Huijuan Song & Yanbo Hu. (2020) On a regularity result for the transonic pressure-gradient system in gas dynamics. Journal of Mathematical Analysis and Applications 481:2, pages 123495.
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Mahmoud A. E. Abdelrahman & G. M. Bahaa. (2019) Elementary waves, Riemann problem, Riemann invariants and new conservation laws for the pressure gradient model. The European Physical Journal Plus 134:5.
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Neelam Gupta & V. D. Sharma. (2016) Diffraction of a weak shock by a wedge in a van der Waals gas. IMA Journal of Applied Mathematics 81:5, pages 824-841.
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Qin Wang & Kyungwoo Song. (2015) The regularity of sonic curves for the two-dimensional Riemann problems of the nonlinear wave system of Chaplygin gas. Discrete and Continuous Dynamical Systems 36:3, pages 1661-1675.
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Li Jun, Ingo Witt & Yin Huicheng. (2015) On the blowup and lifespan of smooth solutions to a class of 2-D nonlinear wave equations with small initial data. Quarterly of Applied Mathematics 73:2, pages 219-251.
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Yicheng Pang, Jianjun Paul Tian & Hanchun Yang. (2012) Two-dimensional Riemann problem for a hyperbolic system of conservation laws in three pieces. Applied Mathematics and Computation 219:4, pages 1695-1711.
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Ding Bingbing & Yin Huicheng. (2012) On the blowup of classical solutions to the 3-D pressure-gradient systems. Journal of Differential Equations 252:5, pages 3608-3629.
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Fengbai Li & Wei Xiao. (2012) Interaction of four rarefaction waves in the bi-symmetric class of the pressure-gradient system. Journal of Differential Equations 252:6, pages 3920-3952.
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Li-Zhen Wang & Qing Huang. (2011) Symmetries and Group-Invariant Solutions for Transonic Pressure-Gradient Equations. Communications in Theoretical Physics 56:2, pages 199-206.
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Zhonghai Xu, Zhenguo Feng & Jiashan Zheng. (2011) Existence and regularity of the solution of a mixed boundary value problem for the Keldysh equation with a nonlinear absorption term. Nonlinear Analysis: Theory, Methods & Applications 74:1, pages 1-8.
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Kyung-Woo Song. (2010) SELF-SIMILAR SOLUTIONS FOR THE 2-D BURGERS SYSTEM IN INFINITE SUBSONIC CHANNELS. Bulletin of the Korean Mathematical Society 47:1, pages 29-37.
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Seunghoon Bang. (2009) Interaction of three and four rarefaction waves of the pressure-gradient system. Journal of Differential Equations 246:2, pages 453-481.
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Zhen Lei & Yuxi Zheng. (2007) A complete global solution to the pressure gradient equation. Journal of Differential Equations 236:1, pages 280-292.
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Zhonghai Xu. (2007) A linear approximation for the regular reflection of a weak shock at a wedge satisfying sonic condition. Journal of Mathematical Analysis and Applications 326:2, pages 1046-1060.
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Zhonghai Xu. (2006) A linear approximation for the regular reflection of a weak shock at a wedge. Journal of Mathematical Analysis and Applications 322:2, pages 712-728.
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Yuxi Zheng. (2006) Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws. Acta Mathematicae Applicatae Sinica, English Series 22:2, pages 177-210.
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Hanchun Yang & Tong Zhang. (2004) On two-dimensional gas expansion for pressure-gradient equations of Euler system. Journal of Mathematical Analysis and Applications 298:2, pages 523-537.
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Eun Heui Kim & Kyungwoo Song. (2004) Classical solutions for the pressure-gradient equations in non-smooth and non-convex domains. Journal of Mathematical Analysis and Applications 293:2, pages 541-550.
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Yuxi Zheng. (2003) A Global Solution to a Two-dimensional Riemann Problem Involving Shocks as Free Boundaries. Acta Mathematicae Applicatae Sinica, English Series 19:4, pages 559-572.
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Sunčica Čanić, Barbara Lee Keyfitz & Eun Heui Kim. (2001) A free boundary problem for a quasi‐linear degenerate elliptic equation: Regular reflection of weak shocks. Communications on Pure and Applied Mathematics 55:1, pages 71-92.
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