Abstract
A method is given for obtaining exact solutions of certain mixed Cauchy problems for second order nonlinear hyperbolic equations. A detailed study is made using the case of the velocity potential equation corresponding to unsteady, planeparallel flows of a polytropic gas. This method can be applied to a wider class of equations. Some properties of the solutions obtained are studied. An approximate theory of propagation of curvilinear weak shock waves through a uniform background is constructed to illustrate the application. The investigation commenced in [1] is continued.
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