Weakly hyperbolic equations with non-analytic coefficients and lower order terms

@article{Garetto2013WeaklyHE,
title={Weakly hyperbolic equations with non-analytic coefficients and lower order terms},
author={Claudia Garetto and M. Ruzhansky},
journal={Mathematische Annalen},
year={2013},
volume={357},
pages={401-440}
}

In this paper we consider weakly hyperbolic equations of higher orders in arbitrary dimensions with time-dependent coefficients and lower order terms. We prove the Gevrey well-posedness of the Cauchy problem under $$C^k$$-regularity of coefficients of the principal part and natural Levi conditions on lower order terms which may be only continuous. In the case of analytic coefficients in the principal part we establish the $$C^\infty $$ well-posedness. The proofs are based on using the quasi… CONTINUE READING