Cauchy Problem for a Class of Totally Characteristic Hyperbolic Operators with Characteristics of Variable Multiplicity in Gevrey Classes (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 < \frac{&#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 = \frac{&#963}{&#963-1}, then the Cauchy problem (1.1) is wellpooed in B ([0, e], G^{\frac{&#963}{&#963-1}}_{L&sup2}(R^n)) (where e > 0, small enough).