Proceedings of the Japan Academy Series A Mathematical Sciences · 2008 · 29 citations · 10 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsGravitationBoundary ConditionsBoundary-value ProblemsInitial Value ProblemsLagrangian DynamicsLagrangian MechanicsPartial Differential EquationsBoundary ProblemFree-boundary ProblemsGlobal Existence TheoryInitial Boundary ConditionsInitial Value Problem In General RelativityOne-dimensional DynamicsUniqueness In Systems Of Differential EquationsUniqueness Of Solutions
In this paper we consider a system of equations describing the one-dimensional motion of a self-gravitating, radiative and chemically reactive gas having the free-boundary. For arbitrary large, smooth initial data we prove the unique existence, global in time, of a classical solution of the corresponding problem with fixed domain, obtained by the Lagrangian mass transformation.
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