Graduate Thesis Or Dissertation
 

A free boundary value problem for the gas dynamic equations

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  • We discuss a mathematical model arising from the following physical situation. We consider a gas-filled cylinder with a piston at one end whose motion is determined by the pressure of the gas within the cylinder and by external forces. Zero mass flux is assumed at the piston while the mass flux is known at the fixed end. This model leads to a free boundary value problem involving the gas dynamic equations. Existence and uniqueness theorems are presented for the linearized problem and for a special case of the non-linear problem. In the non-linear case, the interaction between shocks and the motion of the free boundary are studied. Finally, numerical algorithms for finding approximate solutions of the linear and non-linear models are suggested and examples are performed.
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