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On the stability of a stellar structure in one dimension. II: The reactive case. (English) Zbl 0882.76025
Summary: We complete in this paper [for part I, see the author, Math. Models Methods Appl. Sci. 6, No. 3, 365-383 (1996; Zbl 0853.76075)] the study of stability of the interface in a free boundary problem for a self-gravitating gas in one space dimension, with an external pressure \(P\), and a Fourier coefficient \(\lambda\), for the thermal flux, including a chemical, self-consistent, reacting process. In the non-radiative limit, we find different possible asymptotic behaviours: if \(\lambda>0\), the gas tends to collapse; if \(\lambda=0\), we show that, when \(P>0\), the solution converges for large time to the isothermal solution of the corresponding stationary problem, while for \(P=0\), under some additional condition connecting the total energy and the mass of the structure, the system is unstable, and the gas tends to fill the space. In the limit of the photon gas, we show that analogous asymptotics hold.

76E20 Stability and instability of geophysical and astrophysical flows
76V05 Reaction effects in flows
85A15 Galactic and stellar structure
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
35Q35 PDEs in connection with fluid mechanics
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