In this paper we analyse the Gevrey well-posedness of the Cauchy problem for weakly hyperbolic equations of general form with time-dependent coefficients. The results involve the order of lower order terms and the number of multiple roots. We also derive the corresponding well-posedness results in the space of Gevrey Beurling ultradistributions.
Published inJournal of Differential Equations
Pages1317 - 1340
CitationGARETTO, C. and RUZHANSKY, M., 2012. On the well-posedness of weakly hyperbolic equations with time-dependent coefficients. Journal of Differential Equations, 253 (5), pp. 1317-1340.
Publisher© Elsevier Inc.
VersionAM (Accepted Manuscript)
NotesThis is the author’s version of a work that was accepted for publication in Journal of Differential Equations. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Differential Equations 2012, 253 (5), URL: http://dx.doi.org/10.1016/j.jde.2012.05.001.