On the stability of stellar structure in one dimension II : the reactive case

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1. [1] GUI-QIANG CHEN, 1992, Global solution to the compressible Navier-Stokes equations for a reacting mixture, SIAM J. Math. Anal. 23, 609-634. Zbl0771.35044MR1158824
2. [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. MR989562
3. [3] F. WILLIAMS, 1983, Combustion theory, Addison-Wesley. 
4. [4] Y. B. ZELDOVITCH, Yu. RAISER, 1966, Physics of shock waves and high temperature hydrodynamic phenomena, Academic Press. 
5. [5] R. KlPPENHAHN, A. WEINGERT, 1994, Stellar structure and évolution, Springer Verlag. 
6. [6] D. KINDERLEHRER, G. STAMPACCHIA, 1980, An introduction to variational inequalities and their applications, Academic Press. Zbl0457.35001MR567696
7. [7] T. NAGASAWA, 1988, On the outer pressure problem of the one-dimensional polytropic ideal gas, Japan J. Appl. Math., 5, 53-85. Zbl0665.76076MR924744
8. [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. Zbl0492.76074
9. [9] S. N. ANTONSEV, A.V. KAZHIKOV, V. N. MONAKHOV, 1990, Boundary value problems in mechanics of non-homogeneous fluids, North Holland. Zbl0696.76001
10. [10] P. BLOTTIAU, S. BOUQUET, J. P. CHIÈZE, 1988, An asymptotic self-similar solution for the gravitational collapse, Astron. Astrophys., 207, 24-36. 
11. [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. Zbl0743.35048MR1039243
12. [12] B. DUCOMET, 1995, Evolution of a self-gravitating Rosseland gas in one dimension, Math. Models and Methods in Appl. Sci, 5, 999-1012. Zbl0838.76079MR1359217
13. [13] B. DUCOMET, 1996, On the stability of a stellar structure in one dimension, Math. Models and Methods in Appl. Sci., 6, 365-383. Zbl0853.76075MR1388712
14. [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. Zbl0693.76075MR973382
15. [15] D. HOFF, 1987, Global existence for ld, compressible isentropic Navier-Stokes equations with large initial data, Trans. Amer. Math. Soc, 303, 169-181. Zbl0656.76064MR896014
16. [16] D. HOFF, 1991, Discontinuous solutions of the Navier-Stokes for compressible flows, Arch. Rational Mech. Anal., 114, 15-46. Zbl0732.35071MR1088275
17. [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. Zbl0762.35085MR1142276
18. [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. Zbl0597.76067MR867555
19. [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. Zbl0611.35070MR870700
20. [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. Zbl0729.76027
21. [21] S. CHANDRASEKHAR, 1957, An Introduction to the Study of Stellar Structure, Dover. Zbl0079.23901MR92663
22. [22] B. DUCOMET, Hydrodynamical models of stars, To appear in Reviews in Mathematical Physics. 
23. [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. Zbl0783.76082MR1227730
24. [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. Zbl0833.35114MR1295943

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