PISTON MOVEMENT IN VISCOUS GAS
Keywords:
piston motion, viscous gas, Lagrangian variables, magnetic field, porous medium, a priori estimates, generalized solutionAbstract
This article examines the one-dimensional motion of a piston of a given mass in a tube filled with a viscous, heat-conducting gas in a porous medium, taking into account an external magnetic field. The mathematical formulation of the hydrodynamic problem is formulated in Lagrangian mass variables as a system of differential equations, closed by initial-boundary conditions and Newton's second law for the piston. Using the method of global a priori estimates and Gronwall's lemma, a theorem for the existence and uniqueness of a generalized solution "in the large" over time is rigorously proven. It is established that the functions of absolute temperature and specific gas volume remain strictly positive and bounded over the entire time interval.
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