We consider the Cauchy problem for first-order systems. Assuming that the set of singular points of the characteristic variety is a smooth manifold and the characteristic values are real and semisimple, we introduce a new class which is strictly hyperbolic in the directions transverse to . If the propagation cone and are compatible, we prove, under some additional conditions, that transversally strictly hyperbolic systems are strongly hyperbolic. On the other hand, if the propagation cone is incompatible with , then transversally strictly hyperbolic systems are much more involved, which is discussed utilizing an interesting example.
"Transversally strictly hyperbolic systems." Kyoto J. Math. 60 (4) 1399 - 1418, December 2020. https://doi.org/10.1215/21562261-2019-0066