On the stability of stellar structure in one dimension II : the reactive case
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 31 (1997) no. 3, p. 381-407
@article{M2AN_1997__31_3_381_0,
     author = {Ducomet, B.},
     title = {On the stability of stellar structure in one dimension II : the reactive case},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {31},
     number = {3},
     year = {1997},
     pages = {381-407},
     zbl = {0882.76025},
     mrnumber = {1451348},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1997__31_3_381_0}
}
On the stability of stellar structure in one dimension II : the reactive case. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 31 (1997) no. 3, pp. 381-407. http://www.numdam.org/item/M2AN_1997__31_3_381_0/

[1] Gui-Qiang Chen, 1992, Global solution to the compressible Navier-Stokes equations for a reacting mixture, SIAM J. Math. Anal. 23, 609-634. | MR 1158824 | Zbl 0771.35044

[2] S. F. Shandarin, Ya. B. Zeldovitch, 1989, The large-scale structure of the universe : Turbulence, intermittency, structures in a self-gravitating medium, Reviews of Modern Physics, 61, 185-220. | MR 989562

[3] F. Williams, 1983, Combustion theory, Addison-Wesley.

[4] Y. B. Zeldovitch, Yu. Raiser, 1966, Physics of shock waves and high temperature hydrodynamic phenomena, Academic Press.

[5] R. Klppenhahn, A. Weingert, 1994, Stellar structure and évolution, Springer Verlag.

[6] D. Kinderlehrer, G. Stampacchia, 1980, An introduction to variational inequalities and their applications, Academic Press. | MR 567696 | Zbl 0457.35001

[7] T. Nagasawa, 1988, On the outer pressure problem of the one-dimensional polytropic ideal gas, Japan J. Appl. Math., 5, 53-85. | MR 924744 | Zbl 0665.76076

[8] V.A. Solonnikov, A. V. Kazhikhov, 1981, Existence theorems for the equations of motion of a compressible viscous fluid, Ann. Rev. Fluid Mech., 13, 79-95. | Zbl 0492.76074

[9] S. N. Antonsev, A.V. Kazhikov, V. N. Monakhov, 1990, Boundary value problems in mechanics of non-homogeneous fluids, North Holland. | Zbl 0696.76001

[10] P. Blottiau, S. Bouquet, J. P. Chièze, 1988, An asymptotic self-similar solution for the gravitational collapse, Astron. Astrophys., 207, 24-36.

[11] T. Makino, B. Perthame, 1990, Sur les solutions à symétrie sphériques de l'équation d'Euler-Poisson pour l'évolution d'étoiles gazeuses, Japan J. Appl Math., 7, 165-170. | MR 1039243 | Zbl 0743.35048

[12] B. Ducomet, 1995, Evolution of a self-gravitating Rosseland gas in one dimension, Math. Models and Methods in Appl. Sci, 5, 999-1012. | MR 1359217 | Zbl 0838.76079

[13] B. Ducomet, 1996, On the stability of a stellar structure in one dimension, Math. Models and Methods in Appl. Sci., 6, 365-383. | MR 1388712 | Zbl 0853.76075

[14] T. Nagasawa, 1988, On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with stress-free condition, Quart. of Appl. Math., 46, 665-679. | MR 973382 | Zbl 0693.76075

[15] D. Hoff, 1987, Global existence for ld, compressible isentropic Navier-Stokes equations with large initial data, Trans. Amer. Math. Soc, 303, 169-181. | MR 896014 | Zbl 0656.76064

[16] D. Hoff, 1991, Discontinuous solutions of the Navier-Stokes for compressible flows, Arch. Rational Mech. Anal., 114, 15-46. | MR 1088275 | Zbl 0732.35071

[17] D. Hoff, 1992, Global well-posedness of the Cauchy problem for the Navier-Stokes equations of non-isentropic flow with discontinuous initial data, Journal of Diff. Equ., 95,33-74. | MR 1142276 | Zbl 0762.35085

[18] D. Serre, 1986, Solutions faible globales des équations de Navier-Stokes pour un fluide compressible, C.R. Acad. Sci. Paris, 303, Série I, 639-642. | MR 867555 | Zbl 0597.76067

[19] D. Serre, 1986, Sur l'équation monodimensionnelle d'un fluide visqueux, compressible et conducteur de la chaleur, C.R. Acad. Sci. Paris, 303, Série I, 703-706. | MR 870700 | Zbl 0611.35070

[20] D. Serre, 1991, Évolution d'une masse finie de fluide en dimension 1, In : Nonlinear Partial Differential Equations, H. Brézis et J. L. Lions Ed., Longman. | Zbl 0729.76027

[21] S. Chandrasekhar, 1957, An Introduction to the Study of Stellar Structure, Dover. | MR 92663 | Zbl 0079.23901

[22] B. Ducomet, Hydrodynamical models of stars, To appear in Reviews in Mathematical Physics.

[23] M. Okada, T. Makino, 1993, Free boundary problem for the equation of spherically symmetric motion of viscous gas, Japan J. Indust. Appl. Math., 10, 219-235. | MR 1227730 | Zbl 0783.76082

[24] K. Mizohata, 1993, Global weak solutions for the equation of isothermal gas around a star, Preprint, Dep. of Inform. Sci., Tokyo Inst. of Technology. | MR 1295943 | Zbl 0833.35114