## 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

Zbl 0562.00004