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Thermalization time in a model of neutron star
1. | DPTA/Service de Physique Nucléaire, CEA, DAM, DIF, F-91297 Arpajon |
2. | Mathematical Institute, Academy of Sciences, Zitna 25, 11567 Prague 1 |
References:
[1] |
M. Bertsch, Asymptotic behavior of solutions of a nonlinear diffusion equation, SIAM J. Appl. Math., 42 (1982), 66-76.
doi: 10.1137/0142005. |
[2] |
J. G. Berryman and C. J. Holland, Asymptotic behavior of the nonlinear diffusion equation $n_t=(n^{-1}n_x)_x$ J. Math. Phys., 23 (1982), 983-987.
doi: 10.1063/1.525466. |
[3] |
S. Chandrasekhar, "An Introduction to the Study of Stellar Structures," Dover, 1967. |
[4] |
H-Y. Chin, "Stellar Physics," Vol. 1, Blaisdell, Waltham, 1968. |
[5] |
S. Claudi and F. R. Guarguaglini, Large time behaviour for the heat equation with absorption and convection, Advances in Appl. Math., 16 (1995), 377-401.
doi: 10.1006/aama.1995.1018. |
[6] |
C. M. Dafermos, "Hyperbolic Conservation Laws in Continuum Physics," Springer-Verlag, Berlin Heidelberg, 2000. |
[7] |
B. Ducomet and Š. Nečasová, On a fluid model of neutron star, Ann. Univ. Ferrara, 55 (2009), 153-193.
doi: 10.1007/s11565-009-0067-3. |
[8] |
E. Feireisl, Front propagation for degenerate parabolic equations, Nonlinear Analysis, 35 (1999), 735-746.
doi: 10.1016/S0362-546X(98)00019-4. |
[9] |
E. Feireisl and H. Petzeltová, On the zero-velocity limit solutions to the Navier-Stokes equations of compressible flow, Manuscripta Mathematica, 97 (1998), 109-116.
doi: 10.1007/s002290050089. |
[10] |
M. Forestini, "Principes fondamentaux de structure stellaire," Gordon and Breach, Overseas Publishers Association, 1999. |
[11] |
H. Fujita-Yashima and R. Benabidallah, Equation à symétrie sphérique d'un gaz visqueux et calorifère avec la surface libre, Annali di Matematica pura ed applicata, 168 (1995), 75-117.
doi: 10.1007/BF01759255. |
[12] |
M. A. Herrero and M. Pierre, The Cauchy problem for $u_t=\Delta u^m$ where $0 |
[13] |
D. Hoff, Global solutions of the Navier - Stokes equations for multidimensional compressible flow with discontiuous initial data, J. Diff. Eqs., 120 (1995), 215-254.
doi: 10.1006/jdeq.1995.1111. |
[14] |
K. Jörgens, "Spectral Theory of Second-Order Ordinary Differential Operators," Matematisk Institut, Aarhus University, Lecture Notes Series N0. 2, 1962/63. |
[15] |
S. Jiang, On the asymptotic behavior of the motion of a viscous heat-conducting one-dimensional real, Math. Z., 190 (1994), 317-336.
doi: 10.1007/BF02572324. |
[16] |
S. Jiang, Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain, Commun. Math. Phys., 178 (1996), 339-374.
doi: 10.1007/BF02099452. |
[17] |
R. Kippenhahn and A. Weigert, "Stellar Structure and Evolution," Springer Verlag, Berlin-Heidelberg, 1994. |
[18] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," AMS Providence, Rhode Island, 1968. |
[19] |
J. M. Lattimer, K. A. Van Riper, M. Prakash and M. Prakash, Rapid cooling and the structure of neutron stars, The Astrophysical Journal, 425 (1994), 802-813.
doi: 10.1086/174025. |
[20] |
C. Monrozeau, J. Margueron and Ň. Sandulescu, Nuclear superfluidity and cooling time of neutron-star crusts, Physical Review, C75 (2007), 065807.
doi: 10.1103/PhysRevC.75.065807. |
[21] |
M. H. Protter and H. F. Weinberger, "Maximum Principles in Differential Equations," Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1967. |
[22] |
G. Savaré and V. Vespri, The asymptotic profile of solutions of a class of doubly nonlinear equations, Nonlinear Analysis, Theory, Methods & Applications, 22 (1994) 1553-1565. |
[23] |
J. L. Vazquez, "Smoothing and Decay Estimates for Nonlinear Diffusion Equations," Oxford University Press, Oxford, 2006. |
[24] |
J. L. Vazquez, "The Porous Medium Equation," Clarendon Press, Oxford, 2007. |
[25] |
Z. Wu, J. Zhao, J. Yin and H. Li, "Nonlinear Diffusion Equations," World Scientific, New Jersey, London, Singapore, Hong-Kong, 2001. |
show all references
References:
[1] |
M. Bertsch, Asymptotic behavior of solutions of a nonlinear diffusion equation, SIAM J. Appl. Math., 42 (1982), 66-76.
doi: 10.1137/0142005. |
[2] |
J. G. Berryman and C. J. Holland, Asymptotic behavior of the nonlinear diffusion equation $n_t=(n^{-1}n_x)_x$ J. Math. Phys., 23 (1982), 983-987.
doi: 10.1063/1.525466. |
[3] |
S. Chandrasekhar, "An Introduction to the Study of Stellar Structures," Dover, 1967. |
[4] |
H-Y. Chin, "Stellar Physics," Vol. 1, Blaisdell, Waltham, 1968. |
[5] |
S. Claudi and F. R. Guarguaglini, Large time behaviour for the heat equation with absorption and convection, Advances in Appl. Math., 16 (1995), 377-401.
doi: 10.1006/aama.1995.1018. |
[6] |
C. M. Dafermos, "Hyperbolic Conservation Laws in Continuum Physics," Springer-Verlag, Berlin Heidelberg, 2000. |
[7] |
B. Ducomet and Š. Nečasová, On a fluid model of neutron star, Ann. Univ. Ferrara, 55 (2009), 153-193.
doi: 10.1007/s11565-009-0067-3. |
[8] |
E. Feireisl, Front propagation for degenerate parabolic equations, Nonlinear Analysis, 35 (1999), 735-746.
doi: 10.1016/S0362-546X(98)00019-4. |
[9] |
E. Feireisl and H. Petzeltová, On the zero-velocity limit solutions to the Navier-Stokes equations of compressible flow, Manuscripta Mathematica, 97 (1998), 109-116.
doi: 10.1007/s002290050089. |
[10] |
M. Forestini, "Principes fondamentaux de structure stellaire," Gordon and Breach, Overseas Publishers Association, 1999. |
[11] |
H. Fujita-Yashima and R. Benabidallah, Equation à symétrie sphérique d'un gaz visqueux et calorifère avec la surface libre, Annali di Matematica pura ed applicata, 168 (1995), 75-117.
doi: 10.1007/BF01759255. |
[12] |
M. A. Herrero and M. Pierre, The Cauchy problem for $u_t=\Delta u^m$ where $0 |
[13] |
D. Hoff, Global solutions of the Navier - Stokes equations for multidimensional compressible flow with discontiuous initial data, J. Diff. Eqs., 120 (1995), 215-254.
doi: 10.1006/jdeq.1995.1111. |
[14] |
K. Jörgens, "Spectral Theory of Second-Order Ordinary Differential Operators," Matematisk Institut, Aarhus University, Lecture Notes Series N0. 2, 1962/63. |
[15] |
S. Jiang, On the asymptotic behavior of the motion of a viscous heat-conducting one-dimensional real, Math. Z., 190 (1994), 317-336.
doi: 10.1007/BF02572324. |
[16] |
S. Jiang, Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain, Commun. Math. Phys., 178 (1996), 339-374.
doi: 10.1007/BF02099452. |
[17] |
R. Kippenhahn and A. Weigert, "Stellar Structure and Evolution," Springer Verlag, Berlin-Heidelberg, 1994. |
[18] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," AMS Providence, Rhode Island, 1968. |
[19] |
J. M. Lattimer, K. A. Van Riper, M. Prakash and M. Prakash, Rapid cooling and the structure of neutron stars, The Astrophysical Journal, 425 (1994), 802-813.
doi: 10.1086/174025. |
[20] |
C. Monrozeau, J. Margueron and Ň. Sandulescu, Nuclear superfluidity and cooling time of neutron-star crusts, Physical Review, C75 (2007), 065807.
doi: 10.1103/PhysRevC.75.065807. |
[21] |
M. H. Protter and H. F. Weinberger, "Maximum Principles in Differential Equations," Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1967. |
[22] |
G. Savaré and V. Vespri, The asymptotic profile of solutions of a class of doubly nonlinear equations, Nonlinear Analysis, Theory, Methods & Applications, 22 (1994) 1553-1565. |
[23] |
J. L. Vazquez, "Smoothing and Decay Estimates for Nonlinear Diffusion Equations," Oxford University Press, Oxford, 2006. |
[24] |
J. L. Vazquez, "The Porous Medium Equation," Clarendon Press, Oxford, 2007. |
[25] |
Z. Wu, J. Zhao, J. Yin and H. Li, "Nonlinear Diffusion Equations," World Scientific, New Jersey, London, Singapore, Hong-Kong, 2001. |
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