Well-posedness of hyperbolic systems with multiplicities and smooth coefficients

作者：Garetto Claudia^*; Jah Christian

来源：Mathematische Annalen, 2017, 369(1-2): 441-485.

DOI：10.1007/s00208-016-1436-8

We study hyperbolic systems with multiplicities and smooth coefficients. In the case of non-analytic, smooth coefficients, we prove well-posedness in any Gevrey class and when the coefficients are analytic, we prove well-posedness. The proof is based on a transformation to block Sylvester form introduced by D'Ancona and Spagnolo (Boll UMI 8(1B):169-185, 1998) which increases the system size but does not change the eigenvalues. This reduction introduces lower order terms for which appropriate Levi-type conditions are found. These translate then into conditions on the original coefficient matrix. This paper can be considered as a generalisation of Garetto and Ruzhansky (Math Ann 357(2):401-440, 2013), where weakly hyperbolic higher order equations with lower order terms were considered.

• 出版日期2017-10