We consider the semilinear hyperbolic equations of the form
with entire analytic, where the characteristic roots satisfy
We prove that, if the 's are analytic functions, al the solutions bounded in enjoy the propagation of analyticity; while, if the 's are functions, such a property holds for those solutions which are bounded in some Gevrey class.
Cite this article
Sergio Spagnolo, Propagation of analyticity for a class of nonlinear hyperbolic equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 22 (2011), no. 2, pp. 135–149DOI 10.4171/RLM/591