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Global solution to the one-dimensional equations for a self-gravitating viscous radiative and reactive gas. (English) Zbl 1119.35070
The authors investigate the one-dimensional motion of a compressible, viscous and heat-conducting gas driven by self-gravitation in the free-boundary case. Also, the gas is assumed to be radiative and reactive. Lagrangian mass coordinates are introduced in order to reduce this free-boundary problem to a problem in a fixed domain with an explicit gravitational term. This analysis is based on fundamental local existence results and various a priori estimates. By using them a classical unique global solution could be constructed.

MSC:
35Q35 PDEs in connection with fluid mechanics
76N15 Gas dynamics (general theory)
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
35R35 Free boundary problems for PDEs
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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