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Asymptotic behavior for solutions of some integral equations
Asymptotic behavior of solutions to a model system of a radiating gas
1. | Faculty of Mathematics, Kyushu University, Fukuoka 819-0395, Japan |
References:
[1] |
R. Courant and K. O. Friedrichs, "Supersonic Flow and Shock Waves,", Interscience Publishers, (1948).
|
[2] |
M. Di Francesco, Initial value problem and relaxation limits of the Hamer model for radiating gases in several space variables,, NoDEA Nonl. Differential Equations Appl., 13 (2007), 531.
doi: doi:10.1007/s00030-006-4023-y. |
[3] |
M. Di Francesco, "Diffusive Behavior and Asymptotic Self similarity for Fluid Models,", Ph. D thesis, (2004). Google Scholar |
[4] |
M. Di Francesco and C. Lattanzio, Optimal $L^1$ rate of decay to diffusion waves for the Hamer model of radiating gases,, Appl. Math. Lett., 19 (2006), 1046.
doi: doi:10.1016/j.aml.2004.11.008. |
[5] |
R. Duan, K. Fellner and C. Zhu, Energy method for multi-dimensional balance laws with non-local dissipation,, to appear in J. Math. Pur. Appl. (http://homepage.univie.ac.at/klemens.fellner/preprints/DZFfinal.pdf)., (). Google Scholar |
[6] |
W. L. Gao, L. Z. Ruan and C. J. 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.
doi: doi:10.1016/j.jde.2008.02.023. |
[7] |
W. L. Gao and C. J. Zhu, Asymptotic decay toward the planar rarefaction waves for a model system of the radiating gas in two dimensions,, Math. Models Methods Appl. Sci., 18 (2008), 511.
doi: doi:10.1142/S0218202508002760. |
[8] |
K. Hamer, Nonlinear effects on the propogation of sound waves in a radiating gas,, Quart. J. Mech. Appl. Math., 24 (1971), 155.
doi: doi:10.1093/qjmam/24.2.155. |
[9] |
T. Iguchi and S. Kawashima, On space-time decay properties of solutions to hyperbolic-elliptic coupled systems,, Hiroshima Math. J., 32 (2002), 229.
|
[10] |
S. Kawashima, Y. Nikkuni and S. Nishibata, The initial value problem for hyperbolic-elliptic coupled systems and applications to radiation hydrodynamics,, in, (1998), 87.
|
[11] |
S. Kawashima, Y. Nikkuni and S. Nishibata, Large-time behavior of solutions to hyperbolic-elliptic coupled systems,, Arch. Rational Mech. Anal., 170 (2003), 297.
doi: doi:10.1007/s00205-003-0273-6. |
[12] |
S. Kawashima and S. Nishibata, Shock waves for a model system of the radiating gas,, SIAM J. Math. Anal., 30 (1999), 95.
doi: doi:10.1137/S0036141097322169. |
[13] |
S. Kawashima and S. Nishibata, Weak solutions with a shock to a model system of the radiating gas,, Sci. Bull. Josai. Univ., 5 (1998), 119.
|
[14] |
S. Kawashima and S. Nishibata, Cauchy problem for a model system of the radiating gas: weak solution with a jump and classical solutions,, Math. Models Methods Appl. Sci., 9 (1999), 69.
doi: doi:10.1142/S0218202599000063. |
[15] |
S. Kawashima and S. Nishibata, A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics,, Indiana Univ. Math. J., 50 (2001), 567.
doi: doi:10.1512/iumj.2001.50.1797. |
[16] |
S. Kawashima and Y. Tanaka, Stability of rarefaction waves for a model system of a radiating gas,, Kyushu J. Math., 58 (2004), 211.
doi: doi:10.2206/kyushujm.58.211. |
[17] |
C. Lattanzio and P. Marcati, Global well-posedness and relaxation limits of a model for radiating gas,, J. Differential Equations, 190 (2003), 439.
doi: doi:10.1016/S0022-0396(02)00158-4. |
[18] |
C. Lattanzio, C. Mascia, T. Nguyen, R.G. Plaza and K. Zumbrun, Stability of scalar radiative shock profiles,, SIAM J. Math. Anal., 41 (): 2165.
doi: doi:10.1137/09076026X. |
[19] |
C. Lattanzio, C. Mascia and D. Serre, Shock waves for radiative hyperbolic-elliptic systems,, Indiana Univ. Math. J., 56 (2007), 2601.
doi: doi:10.1512/iumj.2007.56.3043. |
[20] |
C. Lattanzio, C. Mascia and D. Serre, in "Hyperbolic Problems: Theory, Numerics, Applications", (Lyon, (1721), 661. Google Scholar |
[21] |
P. Laurencot, Asymptotic self-similarity for a simplified model for radiating gases,, Asymptot. Anal., 42 (2005), 251.
|
[22] |
C. Lin, J.-F. Coulombel and T. Goudon, Shock profiles for non-equilibrium radiating gases,, Phys. D, 218 (2006), 83.
doi: doi:10.1016/j.physd.2006.04.012. |
[23] |
C. Lin, J.-F. Coulombel and T. Goudon, Asymptotic stability of shock profiles in radiative hydrodynamics,, C. R. Math. Acad. Sci. Paris, 345 (2007), 625.
|
[24] |
Y. Liu and S. Kawashima, Global existence and asymptotic behavior of solutions for quasi-linear dissipative plate equation,, preprint, (). Google Scholar |
[25] |
H. Liu and E. Tadmor, Critical thresholds in a convolution model for nonlinear conservation laws,, SIAM J. Math. Anal., 33 (2001), 930.
|
[26] |
T. Nguyen, R. G. Plaza and K. Zumbrun, Stability of radiative shock profiles for hyperbolic-elliptic coupled systems,, Phys. D, 239 (2010), 428.
doi: doi:10.1016/j.physd.2010.01.011. |
[27] |
S. Nishibata, Asymptotic behavior of solutions to a model system of a radiating gas with discontinuous initial data,, Math. Models Methods Appl. Sci., 10 (2000), 1209.
doi: doi:10.1142/S0218202500000598. |
[28] |
M. Nishikawa and S. Nishibata, Convergence rates toward the travelling waves for a model system of the radiating gas,, Math. Meth. Appl. Sci., 30 (2007), 649.
doi: doi:10.1002/mma.800. |
[29] |
L. Z. Ruan and C. J. Zhu, Asymptotic behavior of solutions to a hyperbolic-elliptic coupled system in multi-dimensional radiating gas,, preprint., (). Google Scholar |
[30] |
S. Schochet and E. Tadmor, The regularized Chapman-Enskog expansion for scalar conservation laws,, Arch. Rational Mech. Anal., 119 (1992), 95.
doi: doi:10.1007/BF00375117. |
[31] |
D. Serre, $L^1$-stability of constants in a model for radiating gases,, Comm. Math. Sci., 1 (2003), 197.
|
[32] |
D. Serre, $L^1$-stability of nonlinear waves in scalar conservation laws,, in, ().
|
[33] |
W. G. Vincenti and C. H. Kruger, "Introduction to Physical Gas Dynamics,", Wiley, (1965). Google Scholar |
[34] |
W. Wang and W. Wang, The pointwise estimates of solutions for a model system of the radiating gas in multi-dimensions,, Nonlinear Analysis, 71 (2009), 1180.
doi: doi:10.1016/j.na.2008.11.050. |
show all references
References:
[1] |
R. Courant and K. O. Friedrichs, "Supersonic Flow and Shock Waves,", Interscience Publishers, (1948).
|
[2] |
M. Di Francesco, Initial value problem and relaxation limits of the Hamer model for radiating gases in several space variables,, NoDEA Nonl. Differential Equations Appl., 13 (2007), 531.
doi: doi:10.1007/s00030-006-4023-y. |
[3] |
M. Di Francesco, "Diffusive Behavior and Asymptotic Self similarity for Fluid Models,", Ph. D thesis, (2004). Google Scholar |
[4] |
M. Di Francesco and C. Lattanzio, Optimal $L^1$ rate of decay to diffusion waves for the Hamer model of radiating gases,, Appl. Math. Lett., 19 (2006), 1046.
doi: doi:10.1016/j.aml.2004.11.008. |
[5] |
R. Duan, K. Fellner and C. Zhu, Energy method for multi-dimensional balance laws with non-local dissipation,, to appear in J. Math. Pur. Appl. (http://homepage.univie.ac.at/klemens.fellner/preprints/DZFfinal.pdf)., (). Google Scholar |
[6] |
W. L. Gao, L. Z. Ruan and C. J. 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.
doi: doi:10.1016/j.jde.2008.02.023. |
[7] |
W. L. Gao and C. J. Zhu, Asymptotic decay toward the planar rarefaction waves for a model system of the radiating gas in two dimensions,, Math. Models Methods Appl. Sci., 18 (2008), 511.
doi: doi:10.1142/S0218202508002760. |
[8] |
K. Hamer, Nonlinear effects on the propogation of sound waves in a radiating gas,, Quart. J. Mech. Appl. Math., 24 (1971), 155.
doi: doi:10.1093/qjmam/24.2.155. |
[9] |
T. Iguchi and S. Kawashima, On space-time decay properties of solutions to hyperbolic-elliptic coupled systems,, Hiroshima Math. J., 32 (2002), 229.
|
[10] |
S. Kawashima, Y. Nikkuni and S. Nishibata, The initial value problem for hyperbolic-elliptic coupled systems and applications to radiation hydrodynamics,, in, (1998), 87.
|
[11] |
S. Kawashima, Y. Nikkuni and S. Nishibata, Large-time behavior of solutions to hyperbolic-elliptic coupled systems,, Arch. Rational Mech. Anal., 170 (2003), 297.
doi: doi:10.1007/s00205-003-0273-6. |
[12] |
S. Kawashima and S. Nishibata, Shock waves for a model system of the radiating gas,, SIAM J. Math. Anal., 30 (1999), 95.
doi: doi:10.1137/S0036141097322169. |
[13] |
S. Kawashima and S. Nishibata, Weak solutions with a shock to a model system of the radiating gas,, Sci. Bull. Josai. Univ., 5 (1998), 119.
|
[14] |
S. Kawashima and S. Nishibata, Cauchy problem for a model system of the radiating gas: weak solution with a jump and classical solutions,, Math. Models Methods Appl. Sci., 9 (1999), 69.
doi: doi:10.1142/S0218202599000063. |
[15] |
S. Kawashima and S. Nishibata, A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics,, Indiana Univ. Math. J., 50 (2001), 567.
doi: doi:10.1512/iumj.2001.50.1797. |
[16] |
S. Kawashima and Y. Tanaka, Stability of rarefaction waves for a model system of a radiating gas,, Kyushu J. Math., 58 (2004), 211.
doi: doi:10.2206/kyushujm.58.211. |
[17] |
C. Lattanzio and P. Marcati, Global well-posedness and relaxation limits of a model for radiating gas,, J. Differential Equations, 190 (2003), 439.
doi: doi:10.1016/S0022-0396(02)00158-4. |
[18] |
C. Lattanzio, C. Mascia, T. Nguyen, R.G. Plaza and K. Zumbrun, Stability of scalar radiative shock profiles,, SIAM J. Math. Anal., 41 (): 2165.
doi: doi:10.1137/09076026X. |
[19] |
C. Lattanzio, C. Mascia and D. Serre, Shock waves for radiative hyperbolic-elliptic systems,, Indiana Univ. Math. J., 56 (2007), 2601.
doi: doi:10.1512/iumj.2007.56.3043. |
[20] |
C. Lattanzio, C. Mascia and D. Serre, in "Hyperbolic Problems: Theory, Numerics, Applications", (Lyon, (1721), 661. Google Scholar |
[21] |
P. Laurencot, Asymptotic self-similarity for a simplified model for radiating gases,, Asymptot. Anal., 42 (2005), 251.
|
[22] |
C. Lin, J.-F. Coulombel and T. Goudon, Shock profiles for non-equilibrium radiating gases,, Phys. D, 218 (2006), 83.
doi: doi:10.1016/j.physd.2006.04.012. |
[23] |
C. Lin, J.-F. Coulombel and T. Goudon, Asymptotic stability of shock profiles in radiative hydrodynamics,, C. R. Math. Acad. Sci. Paris, 345 (2007), 625.
|
[24] |
Y. Liu and S. Kawashima, Global existence and asymptotic behavior of solutions for quasi-linear dissipative plate equation,, preprint, (). Google Scholar |
[25] |
H. Liu and E. Tadmor, Critical thresholds in a convolution model for nonlinear conservation laws,, SIAM J. Math. Anal., 33 (2001), 930.
|
[26] |
T. Nguyen, R. G. Plaza and K. Zumbrun, Stability of radiative shock profiles for hyperbolic-elliptic coupled systems,, Phys. D, 239 (2010), 428.
doi: doi:10.1016/j.physd.2010.01.011. |
[27] |
S. Nishibata, Asymptotic behavior of solutions to a model system of a radiating gas with discontinuous initial data,, Math. Models Methods Appl. Sci., 10 (2000), 1209.
doi: doi:10.1142/S0218202500000598. |
[28] |
M. Nishikawa and S. Nishibata, Convergence rates toward the travelling waves for a model system of the radiating gas,, Math. Meth. Appl. Sci., 30 (2007), 649.
doi: doi:10.1002/mma.800. |
[29] |
L. Z. Ruan and C. J. Zhu, Asymptotic behavior of solutions to a hyperbolic-elliptic coupled system in multi-dimensional radiating gas,, preprint., (). Google Scholar |
[30] |
S. Schochet and E. Tadmor, The regularized Chapman-Enskog expansion for scalar conservation laws,, Arch. Rational Mech. Anal., 119 (1992), 95.
doi: doi:10.1007/BF00375117. |
[31] |
D. Serre, $L^1$-stability of constants in a model for radiating gases,, Comm. Math. Sci., 1 (2003), 197.
|
[32] |
D. Serre, $L^1$-stability of nonlinear waves in scalar conservation laws,, in, ().
|
[33] |
W. G. Vincenti and C. H. Kruger, "Introduction to Physical Gas Dynamics,", Wiley, (1965). Google Scholar |
[34] |
W. Wang and W. Wang, The pointwise estimates of solutions for a model system of the radiating gas in multi-dimensions,, Nonlinear Analysis, 71 (2009), 1180.
doi: doi:10.1016/j.na.2008.11.050. |
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