Propagation of analyticity of solutions to the Cauchy problem for weakly hyperbolic semi-linear equations (Q1848098)

This paper deals with an \(m\)-order weakly hyperbolic partial differential operator with constant coefficients \(P({\mathcal D})\). In Theorem 1.1 an a priori estimate in appropriate Gevrey classes is shown. This estimate enables the author to prove in Theorem 1.2 a local existence result in time to the Cauchy problem for a semilinear operator having \(P({\mathcal D})\) as a principal part. Under several additional conditions a propagation of the analyticity theorem is shown, i.e. the analyticity of the initial conditions everywhere in \(\mathbb{R}^n\) implies the analyticity of the solution of the corresponding Cauchy problem for any \((t,x)\in [0,T]\times \mathbb{R}^n\), \(T>0\).