@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}, volume = {31}, year = {1997}, pages = {381-407}, mrnumber = {1451348}, zbl = {0882.76025}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_1997__31_3_381_0} }
Ducomet, B. On the stability of stellar structure in one dimension II : the reactive case. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 31 (1997) pp. 381-407. http://gdmltest.u-ga.fr/item/M2AN_1997__31_3_381_0/
[1] Global solution to the compressible Navier-Stokes equations for a reacting mixture, SIAM J. Math. Anal. 23, 609-634. | MR 1158824 | Zbl 0771.35044
, 1992,[2] The large-scale structure of the universe : Turbulence, intermittency, structures in a self-gravitating medium, Reviews of Modern Physics, 61, 185-220. | MR 989562
, , 1989,[3] Combustion theory, Addison-Wesley.
, 1983,[4] Physics of shock waves and high temperature hydrodynamic phenomena, Academic Press.
, , 1966,[5] Stellar structure and évolution, Springer Verlag.
, , 1994,[6] An introduction to variational inequalities and their applications, Academic Press. | MR 567696 | Zbl 0457.35001
, , 1980,[7] On the outer pressure problem of the one-dimensional polytropic ideal gas, Japan J. Appl. Math., 5, 53-85. | MR 924744 | Zbl 0665.76076
, 1988,[8] Existence theorems for the equations of motion of a compressible viscous fluid, Ann. Rev. Fluid Mech., 13, 79-95. | Zbl 0492.76074
, , 1981,[9] Boundary value problems in mechanics of non-homogeneous fluids, North Holland. | Zbl 0696.76001
, , , 1990,[10] An asymptotic self-similar solution for the gravitational collapse, Astron. Astrophys., 207, 24-36.
, , , 1988,[11] 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
, , 1990,[12] 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
, 1995,[13] 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
, 1996,[14] 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
, 1988,[15] 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
, 1987,[16] Discontinuous solutions of the Navier-Stokes for compressible flows, Arch. Rational Mech. Anal., 114, 15-46. | MR 1088275 | Zbl 0732.35071
, 1991,[17] 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
, 1992,[18] 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
, 1986,[19] 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
, 1986,[20] 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
, 1991,[21] An Introduction to the Study of Stellar Structure, Dover. | MR 92663 | Zbl 0079.23901
, 1957,[22] Hydrodynamical models of stars, To appear in Reviews in Mathematical Physics.
,[23] 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
, , 1993,[24] 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
, 1993,