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Generalized wavefront expansion properties and limitations. (English) Zbl 0609.76067

The properties of an asymptotic method for the study of the propagation of weak shock waves in hyperbolic systems are examined in detail in the simple case of the single nonlinear wave equation in one space dimension.
The general features of the method are briefly recalled and a comparison between the results obtained by this method and the exact solutions obtained by the shockfitting technique is made. Under appropriate regularity assumptions the method provides an approximation of the exact solution of the desired order for short times.

MSC:

76L05 Shock waves and blast waves in fluid mechanics
35L67 Shocks and singularities for hyperbolic equations
76M99 Basic methods in fluid mechanics
76N15 Gas dynamics (general theory)
35L65 Hyperbolic conservation laws
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