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Journal articles on the topic 'Scalar viscous shocks'

Author: Grafiati
Published: 14 March 2023

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1

Bressan, Alberto, and Carlotta Donadello. "On the formation of scalar viscous shocks problem." International Journal of Dynamical Systems and Differential Equations 1, no. 1 (2007): 1. http://dx.doi.org/10.1504/ijdsde.2007.013740.

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2

Stokols, Logan F. "L2-type contraction of viscous shocks for scalar conservation laws." Journal of Hyperbolic Differential Equations 18, no. 02 (June 2021): 271–92. http://dx.doi.org/10.1142/s0219891621500089.

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We study small shocks of 1D scalar viscous conservation laws with uniformly convex flux and nonlinear dissipation. We show that such shocks are [Formula: see text] stable independently of the strength of the dissipation, even with large perturbations. The proof uses the relative entropy method with a spatially-inhomogeneous pseudo-norm.
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3

Kang, Moon-Jin. "L2-type contraction for shocks of scalar viscous conservation laws with strictly convex flux." Journal de Mathématiques Pures et Appliquées 145 (January 2021): 1–43. http://dx.doi.org/10.1016/j.matpur.2020.10.005.

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4

Shixiang, Ma. "Inviscid Limit for Scalar Viscous Conservation Laws in Presence of Strong Shocks and Boundary Layers." Journal of Partial Differential Equations 25, no. 2 (June 2012): 171–86. http://dx.doi.org/10.4208/jpde.v25.n2.4.

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5

Dalibard, Anne-Laure, and Moon-Jin Kang. "Existence and stability of planar shocks of viscous scalar conservation laws with space-periodic flux." Journal de Mathématiques Pures et Appliquées 107, no. 3 (March 2017): 336–66. http://dx.doi.org/10.1016/j.matpur.2016.07.003.

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6

Choi, Kyudong, and Alexis F. Vasseur. "Short-Time Stability of Scalar Viscous Shocks in the Inviscid Limit by the Relative Entropy Method." SIAM Journal on Mathematical Analysis 47, no. 2 (January 2015): 1405–18. http://dx.doi.org/10.1137/140961523.

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7

MEI, MING. "STABILITY OF SHOCK PROFILES FOR NONCONVEX SCALAR VISCOUS CONSERVATION LAWS." Mathematical Models and Methods in Applied Sciences 05, no. 03 (May 1995): 279–96. http://dx.doi.org/10.1142/s0218202595000188.

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This paper is to study the stability of shock profiles for nonconvex scalar viscous conservation laws with the nondegenerate and the degenerate shock conditions by means of an elementary energy method. In both cases, the shock profiles are proved to be asymptotically stable for suitably small initial disturbances. Moreover, in the case of nondegenerate shock condition, time decay rates of asymptotics are also obtained.
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8

Hoff, David, and Kevin Zumbrun. "Asymptotic behavior of multidimensional scalar viscous shock fronts." Indiana University Mathematics Journal 49, no. 2 (2000): 427–74. http://dx.doi.org/10.1512/iumj.2000.49.1942.

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9

Goodman, Jonathan. "Stability of viscous scalar shock fronts in several dimensions." Transactions of the American Mathematical Society 311, no. 2 (February 1, 1989): 683. http://dx.doi.org/10.1090/s0002-9947-1989-0978372-9.

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10

Nishihara, Kenji. "Boundary Effect on a Stationary Viscous Shock Wave for Scalar Viscous Conservation Laws." Journal of Mathematical Analysis and Applications 255, no. 2 (March 2001): 535–50. http://dx.doi.org/10.1006/jmaa.2000.7255.

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11

Deng, ShiJin, and WeiKe Wang. "Pointwise decaying rate of large perturbation around viscous shock for scalar viscous conservation law." Science China Mathematics 56, no. 4 (February 1, 2013): 729–36. http://dx.doi.org/10.1007/s11425-012-4566-9.

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12

Kang, Moon-Jin, and Alexis F. Vasseur. "L2-contraction for shock waves of scalar viscous conservation laws." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 34, no. 1 (January 2017): 139–56. http://dx.doi.org/10.1016/j.anihpc.2015.10.004.

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13

Freist�hler, Heinrich, and Denis Serre. "?1 stability of shock waves in scalar viscous conservation laws." Communications on Pure and Applied Mathematics 51, no. 3 (March 1998): 291–301. http://dx.doi.org/10.1002/(sici)1097-0312(199803)51:3<291::aid-cpa4>3.0.co;2-5.

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14

Hoff, David, and Kevin Zumbrun. "Pointwise Green's Function Bounds for Multidimensional Scalar Viscous Shock Fronts." Journal of Differential Equations 183, no. 2 (August 2002): 368–408. http://dx.doi.org/10.1006/jdeq.2001.4125.

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15

Plaza, Ramón G. "Lp-decay rates for perturbations of degenerate scalar viscous shock waves." Journal of Mathematical Analysis and Applications 382, no. 2 (October 2011): 864–82. http://dx.doi.org/10.1016/j.jmaa.2011.04.091.

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16

NISHIHARA, Kenji, and Huijiang ZHAO. "Convergence rates to viscous shock profile for general scalar viscous conservation laws with large initial disturbance." Journal of the Mathematical Society of Japan 54, no. 2 (April 2002): 447–66. http://dx.doi.org/10.2969/jmsj/05420447.

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17

Shi, Renkun, and Weike Wang. "Nonlinear stability of large perturbation around viscous shock wave for 2-D scalar viscous conservation law." Indiana University Mathematics Journal 65, no. 4 (2016): 1137–82. http://dx.doi.org/10.1512/iumj.2016.65.5850.

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18

Li, Yingwei. "Scalar Green function bounds for instantaneous shock location and one-dimensional stability of viscous shock waves." Quarterly of Applied Mathematics 74, no. 3 (June 16, 2016): 499–538. http://dx.doi.org/10.1090/qam/1431.

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19

Talbot, B., Y. Mammeri, and N. Bedjaoui. "Viscous shock anomaly in a variable-viscosity Burgers flow with an active scalar." Fluid Dynamics Research 47, no. 6 (October 1, 2015): 065502. http://dx.doi.org/10.1088/0169-5983/47/6/065502.

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20

Kang, Moon-Jin, Alexis F. Vasseur, and Yi Wang. "L2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws." Journal of Differential Equations 267, no. 5 (August 2019): 2737–91. http://dx.doi.org/10.1016/j.jde.2019.03.030.

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21

Xin, Zhouping, Qian Yuan, and Yuan Yuan. "Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-D convex scalar viscous conservation laws." Indiana University Mathematics Journal 70, no. 6 (2021): 2295–349. http://dx.doi.org/10.1512/iumj.2021.70.8706.

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22

Liu, Ye-chi. "Time Decay Rate of Solutions Toward the Viscous Shock Waves under Periodic Perturbations for the Scalar Conservation Law with Nonlinear Viscosity." Acta Mathematicae Applicatae Sinica, English Series 39, no. 1 (December 28, 2022): 28–48. http://dx.doi.org/10.1007/s10255-023-1028-9.

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23

Yoshida, Natsumi. "Asymptotic Behavior of Solutions Toward the Viscous Shock Waves to the Cauchy Problem for the Scalar Conservation Law with Nonlinear Flux and Viscosity." SIAM Journal on Mathematical Analysis 50, no. 1 (January 2018): 891–932. http://dx.doi.org/10.1137/17m1118798.

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24

Liu, Yechi. "Time decay rate of solutions toward the viscous shock waves to the Cauchy problem for the scalar conservation law with nonlinear viscosity and discontinuous initial data." Nonlinear Analysis 222 (September 2022): 112945. http://dx.doi.org/10.1016/j.na.2022.112945.

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25

Restrepo, Julián, and José R. Simões-Moreira. "Viscous effects on real gases in quasi-one-dimensional supersonic convergent divergent nozzle flows." Journal of Fluid Mechanics 951 (November 3, 2022). http://dx.doi.org/10.1017/jfm.2022.853.

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Viscous effects on an ideal gas flow in a supersonic convergent–divergent nozzle are a well-studied subject in classical gas dynamics. However, the ideal assumption fails on fluids that exhibit complex behaviours such as near-critical-region and non-ideal dense vapours. Under those conditions, a realistic equation of state (EOS) plays a vital role for a precise and realistic computation. This work examines the problem for solving the quasi-one-dimensional viscous compressible flow using a realistic EOS. The governing equations are discretised and solved using the fourth-order Runge–Kutta method coupled with a state-of-the-art EOS to calculate the thermodynamic properties. The role of the Grüneisen parameter along with viscous and real gas effects and their influence on the sonic point formation are discussed. The study shows that the flow may not achieve the supersonic regime for any pressure ratio depending on the combination of that parameter and the normalised friction factor. In addition, the analysis yields the discharge coefficient and the isentropic nozzle efficiency, which may achieve maximum values as a function of the stagnation conditions. Finally, the study also evaluates the formation and intensity of normal shock waves by using the Rankine–Hugoniot relations, which now depend on the real gas and viscous effects in opposition to the inviscid solution. Moreover, the methodology used captures the sonic point and shock wave position by a space marching algorithm using the Brent method for scalar minimisation. Experimental data available in the open literature corroborate the approach.
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26

Kamin, S., and S. Schochet. "Global asymptotic stability for finite-cross-section planar shock profiles of viscous scalar conservation laws." Differential and Integral Equations 17, no. 7-8 (January 1, 2004). http://dx.doi.org/10.57262/die/1356060330.

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