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General constrained conservation laws. Application to pedestrian flow modeling
Weighted energy method and long wave short wave decomposition on the linearized compressible Navier-Stokes equation
1. | Department of Mathematics, National University of Singapore, Singapore 117543, Singapore |
References:
[1] |
I.-L. Chern and T.-P. Liu, Convergence to diffusion waves of solutions for viscous conservation laws, Comm. Math. Phys., 110 (1987), 503-517.
doi: 10.1007/BF01212425. |
[2] |
I.-L. Chern and T.-P. Liu, Erratum: "Convergence to difision waves of solutions for viscous conservation laws," Comm. Math. Phys., 120 (1989), 525-527. |
[3] |
S. Kawashima, Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications, Proc. Roy. SOC. Edinburgh Sect. A, 106 (1987), 169-194.
doi: 10.1017/S0308210500018308. |
[4] |
T.-P. Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem. American Mathematical Society, 56 (1985). |
[5] |
T.-P. Liu, Interactions of nonlinear hyperbolic waves, in "Nonlinear Analysis" (Taipei, 1989), World Sci. Publ., Teaneck, New Jersey, (1991), 171-183. |
[6] |
T.-P. Liu and S.-H. Yu, The Green's function and large-time behavior of solutions for the one-dimensional Boltzmann equation, Comm. Pure Appl. Math., 57 (2004), 1543-1608.
doi: 10.1002/cpa.20011. |
[7] |
T.-P. Liu and Y. Zeng, Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws, Mem. Amer. Math. Soc., 125 (1997). |
[8] |
T. Umeda, S. Kawashima and Y. Shizuta, On the decay of solutions to the linearized equations of electromagnetofuid dynamics, Japan J. Appl. Math., 1 (1984), 435-457.
doi: 10.1007/BF03167068. |
[9] |
S. Zheng and W. Shen, Global solutions to the Cauchy problem of quasilinear hyperbolic parabolic coupled systems, Scientia Sinica Ser. A, 30 (1987), 1133-1149. |
[10] |
Y. Zeng, $L^1$ asymptotic behavior of compressible, isentropic, viscous 1-D flow, Comm. Pure Appl. Math., 47 (1994), 1053-1082.
doi: 10.1002/cpa.3160470804. |
show all references
References:
[1] |
I.-L. Chern and T.-P. Liu, Convergence to diffusion waves of solutions for viscous conservation laws, Comm. Math. Phys., 110 (1987), 503-517.
doi: 10.1007/BF01212425. |
[2] |
I.-L. Chern and T.-P. Liu, Erratum: "Convergence to difision waves of solutions for viscous conservation laws," Comm. Math. Phys., 120 (1989), 525-527. |
[3] |
S. Kawashima, Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications, Proc. Roy. SOC. Edinburgh Sect. A, 106 (1987), 169-194.
doi: 10.1017/S0308210500018308. |
[4] |
T.-P. Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem. American Mathematical Society, 56 (1985). |
[5] |
T.-P. Liu, Interactions of nonlinear hyperbolic waves, in "Nonlinear Analysis" (Taipei, 1989), World Sci. Publ., Teaneck, New Jersey, (1991), 171-183. |
[6] |
T.-P. Liu and S.-H. Yu, The Green's function and large-time behavior of solutions for the one-dimensional Boltzmann equation, Comm. Pure Appl. Math., 57 (2004), 1543-1608.
doi: 10.1002/cpa.20011. |
[7] |
T.-P. Liu and Y. Zeng, Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws, Mem. Amer. Math. Soc., 125 (1997). |
[8] |
T. Umeda, S. Kawashima and Y. Shizuta, On the decay of solutions to the linearized equations of electromagnetofuid dynamics, Japan J. Appl. Math., 1 (1984), 435-457.
doi: 10.1007/BF03167068. |
[9] |
S. Zheng and W. Shen, Global solutions to the Cauchy problem of quasilinear hyperbolic parabolic coupled systems, Scientia Sinica Ser. A, 30 (1987), 1133-1149. |
[10] |
Y. Zeng, $L^1$ asymptotic behavior of compressible, isentropic, viscous 1-D flow, Comm. Pure Appl. Math., 47 (1994), 1053-1082.
doi: 10.1002/cpa.3160470804. |
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