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Highly oscillatory multidimensional shocks. (English) Zbl 0929.35090

The author considers a nonlinear first-order partial differential equation of hyperbolic type, constructs small oscillating perturbations of certain shock solutions, and shows that such expansions are close to exact shock solutions for small wavelengths. Some assumptions used in the author’s two previous papers [C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 9, 975-980 and 981-986 (1997; Zbl 0891.35094 and Zbl 0891.35095)] on the same topic are no longer needed in the present paper.
Reviewer: T.Aktosun (Fargo)

MSC:

35L67 Shocks and singularities for hyperbolic equations
35L60 First-order nonlinear hyperbolic equations
35C20 Asymptotic expansions of solutions to PDEs
35L65 Hyperbolic conservation laws
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