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Convergence rates towards the traveling waves for a model system of radiating gas with discontinuities
1. | Research Institute of Nonlinear Partial Differential Equations, Organization for University Research Initiatives, Waseda University, 3-4-1 Ohkubo Shinjuku, Tokyo 169-8555, Japan |
References:
[1] |
R. Duan, K. Fellner and C. Zhu, Energy method for multi-dimensional balance laws with non-local dissipation, J. Math. Pures Appl., 93 (2010), 572-598.
doi: 10.1016/j.matpur.2009.10.007. |
[2] |
W. Gao, L. Ruan and C. Zhu, Decay rates to the planar rarefaction waves for a model system of the radiating gas in $n$ dimensions J. Differential Equations, 244 (2008), 2614-2640.
doi: 10.1016/j.jde.2008.02.023. |
[3] |
K. Hamer, Nonlinear effects on the propagation of sounds waves in a radiating gas, Quarter J. Mech. Appl. Math., 24 (1971), 155-168.
doi: 10.1093/qjmam/24.2.155. |
[4] |
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion, Comm. Math. Phys., 101 (1985), 97-127.
doi: 10.1007/BF01212358. |
[5] |
S. Kawashima and S. Nishibata, Weak solutions with a shock to a model system of the radiating gas, Sci. Bull. Josai Univ. special issue, 5 (1998), 119-130. |
[6] |
S. Kawashima and S. Nishibata, Shock waves for a model system of the radiating gas, SIAM J. Math. Anal., 30 (1999), 95-117.
doi: 10.1137/S0036141097322169. |
[7] |
S. Kawashima and S. Nishibata, Cauchy problem for a model system of the radiating gas: Weak solutions with a jump and classical solutions, Math. Models. Meth. Sci., 9 (1999), 69-91. |
[8] |
S. Kawashima, S. Nishibata and P. Zhu, Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space, Comm. Math. Phys., 240 (2003), 483-500. |
[9] |
S. Kawashima and Y. Tanaka, Stability of rarefaction waves for a model system of radiating gas, Kyushu J. Math., 58 (2004), 211-250.
doi: 10.2206/kyushujm.58.211. |
[10] |
S. N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR Sbor., 10 (1970), 217-243.
doi: 10.1070/SM1970v010n02ABEH002156. |
[11] |
C. Lattanzio, C. Mascia, T. Nguyen, R. Plaza and K. Zumbrun, Stability of scalar radiative shock profiles, SIAM J. Math. Anal., 41 (2009), 2165-2206.
doi: 10.1137/09076026X. |
[12] |
A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex nonlinearity, Commun. Math. Phys., 165 (1994), 83-96.
doi: 10.1007/BF02099739. |
[13] |
S. Nishibata, Asymptotic behavior of solutions to a model system of radiating gas with discontinuous initial data, Math. Models. Meth. Appl. Sci., 8 (2000), 1209-1231. |
[14] |
M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws, Funkcialaj Ekvacioj, 41 (1998), 107-132. |
[15] |
M. Nishikawa and S. Nishibata, Convergence rates toward the traveling waves for a model system of the radiating gas, Math. Meth. Appl. Sci., 30 (2007), 649-663.
doi: 10.1002/mma.800. |
[16] |
D. Serre, $L^1$-stability of constants in a model for radiating gases, Comm. Math. Sci., 1 (2003), 197-205. |
[17] |
M. Suzuki, Asymptotic stability of stationary solutions to the Euler-Poisson equations arising in plasma physics, Kinetic Related Models, 4 (2011), 569-588. |
[18] |
W. Wang and W. Wang, The pointwise estimates of solutions for a model system of the radiating gas in multi-dimensions, Nonlinear Anal., 71 (2009), 1180-1195.
doi: 10.1016/j.na.2008.11.050. |
show all references
References:
[1] |
R. Duan, K. Fellner and C. Zhu, Energy method for multi-dimensional balance laws with non-local dissipation, J. Math. Pures Appl., 93 (2010), 572-598.
doi: 10.1016/j.matpur.2009.10.007. |
[2] |
W. Gao, L. Ruan and C. Zhu, Decay rates to the planar rarefaction waves for a model system of the radiating gas in $n$ dimensions J. Differential Equations, 244 (2008), 2614-2640.
doi: 10.1016/j.jde.2008.02.023. |
[3] |
K. Hamer, Nonlinear effects on the propagation of sounds waves in a radiating gas, Quarter J. Mech. Appl. Math., 24 (1971), 155-168.
doi: 10.1093/qjmam/24.2.155. |
[4] |
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion, Comm. Math. Phys., 101 (1985), 97-127.
doi: 10.1007/BF01212358. |
[5] |
S. Kawashima and S. Nishibata, Weak solutions with a shock to a model system of the radiating gas, Sci. Bull. Josai Univ. special issue, 5 (1998), 119-130. |
[6] |
S. Kawashima and S. Nishibata, Shock waves for a model system of the radiating gas, SIAM J. Math. Anal., 30 (1999), 95-117.
doi: 10.1137/S0036141097322169. |
[7] |
S. Kawashima and S. Nishibata, Cauchy problem for a model system of the radiating gas: Weak solutions with a jump and classical solutions, Math. Models. Meth. Sci., 9 (1999), 69-91. |
[8] |
S. Kawashima, S. Nishibata and P. Zhu, Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space, Comm. Math. Phys., 240 (2003), 483-500. |
[9] |
S. Kawashima and Y. Tanaka, Stability of rarefaction waves for a model system of radiating gas, Kyushu J. Math., 58 (2004), 211-250.
doi: 10.2206/kyushujm.58.211. |
[10] |
S. N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR Sbor., 10 (1970), 217-243.
doi: 10.1070/SM1970v010n02ABEH002156. |
[11] |
C. Lattanzio, C. Mascia, T. Nguyen, R. Plaza and K. Zumbrun, Stability of scalar radiative shock profiles, SIAM J. Math. Anal., 41 (2009), 2165-2206.
doi: 10.1137/09076026X. |
[12] |
A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex nonlinearity, Commun. Math. Phys., 165 (1994), 83-96.
doi: 10.1007/BF02099739. |
[13] |
S. Nishibata, Asymptotic behavior of solutions to a model system of radiating gas with discontinuous initial data, Math. Models. Meth. Appl. Sci., 8 (2000), 1209-1231. |
[14] |
M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws, Funkcialaj Ekvacioj, 41 (1998), 107-132. |
[15] |
M. Nishikawa and S. Nishibata, Convergence rates toward the traveling waves for a model system of the radiating gas, Math. Meth. Appl. Sci., 30 (2007), 649-663.
doi: 10.1002/mma.800. |
[16] |
D. Serre, $L^1$-stability of constants in a model for radiating gases, Comm. Math. Sci., 1 (2003), 197-205. |
[17] |
M. Suzuki, Asymptotic stability of stationary solutions to the Euler-Poisson equations arising in plasma physics, Kinetic Related Models, 4 (2011), 569-588. |
[18] |
W. Wang and W. Wang, The pointwise estimates of solutions for a model system of the radiating gas in multi-dimensions, Nonlinear Anal., 71 (2009), 1180-1195.
doi: 10.1016/j.na.2008.11.050. |
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