(untitled) (Journal of Partial Differential Equations, 2018)
This paper studies tho Cauchy problem of totally characteristic hyperbolic operator (1.1) in Gevrey classes, and obtains the following main result: Under the conditions (I) - (VI), if 1 &#8804 s < &#963&#963-1 (&#963 is definded by (1.7)). then the Cauchy problem (1.1) is wellposed in B ([0, T], G^s_L&sup2, (R^n)); if s = &#963&#963-1, then the Cauchy problem (1.1) is wellpooed in B ([0, e], G^&#963&#963-1 _L&sup2(R^n)) (where e > 0, small enough).