×

zbMATH — the first resource for mathematics

Propagation of smoothness for nonlinear second-order strictly hyperbolic differential equations. (English) Zbl 0575.35062
Pseudodifferential operators and applications, Proc. Symp., Notre Dame/Indiana 1984, Proc. Symp. Pure Math. 43, 21-44 (1985).
[For the entire collection see Zbl 0562.00004.]
The author analyses the order of the anomalous singularities occurring in solutions of nonlinear second-order, strictly hyperbolic equations, and provides complete proofs for the general semilinear equations \(p_ 2(x,D)u=f(x,u)\) and \(p_ 2(x,D)u=f(x,u,Du),\) with f smooth, as well as an outline of the proof in the quasilinear case.
Reviewer: A.D.Osborne

MSC:
35L70 Second-order nonlinear hyperbolic equations
35L67 Shocks and singularities for hyperbolic equations