GARETTO, C. and RUZHANSKY, M., 2016. On C ∞ well-posedness of hyperbolic systems with multiplicities. arXiv:1512.06243v2 [math.AP]
In this paper we study first order hyperbolic systems with multiple
characteristics (weakly hyperbolic) and time-dependent analytic coefficients. The
main question is when the Cauchy problem for such systems is well-posed in C∞
and in D′. We prove that the analyticity of the coefficients combined with suitable
hypotheses on the eigenvalues guarantee the C∞ well-posedness of the corresponding
Cauchy problem. This result is an extension to systems of the analogous results
for scalar equations recently obtained by Jannelli and Taglialatela in  and by
the authors in .
This pre-print was submitted to arXiv on 11 January 2016.