Self-Semilar Solutions of Hydrodynamic Equations for Expanding Layer with Boundary Condition Specified by Differential Equation

概要

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A set of self-similar solutions of the hydrodynamic partially differencial equations are derived for an expanding layer. The equations consist of continuity, momentum and energy equations. Energy is supplied into the layer constantly in time and homogeneously in space. One end surface of the layer is fixed in the space and the motion of the other end is specified by a partially differential equation. By using a similar variable, the equations are transformed to a set of ordinary differential equations. Forms of these ordinary differential equations and hence the self-similar solutions are not unique according to the choice of similar variables. However, the solutions themselves as functions of time and space are shown to be unique.
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