Quasilinear weakly hyperbolic equations with Levi's conditions

This paper deals with quasilinear weakly hyperbolic equations satisfying the Levi condition. The authors introduce in the quasi-linear case the notions of weakly hyperbolic equation of constant multiplicity, Levi's condition and domain of influence. The solution $u$ of the corresponding equation is assumed to be real-valued and to belong to $C^\infty(\Omega)$, while the equation depends analytically on $(y,u^{(\beta)}(y)), y\in\Omega$. According to the main result of this paper, analyticity propagates across an analytic hypersurface $S_0$ into the domain of influence based on $S_0$. This paper is a continuation of some previous investigations of the same authors.