Abstract
This paper studies spherical detonation waves in relativistic hydrodynamics, which are of some interest for cosmology. We prove that the spherical detonation wave propagating in an unburnt fluid at rest after a sudden explosion must be a Chapman–Jouguet detonation (CJDT) wave. We give a detailed structure for the CJDT wave solution. This paper also study detonation wave solutions of a spherical piston problem which describes the wave motion produced by a sphere expanding with a constant speed. We use self-similarity to reduce the spherical piston problem to a boundary value problem for a system of nonlinear ordinary differential equations. Global existence of self-similar detonation wave solutions to the spherical piston problem is obtained constructively.
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