TY - JOUR
T1 - Cauchy Problem for a Class of Totally Characteristic Hyperbolic Operators with Characteristics of Variable Multiplicity in Gevrey Classes
JO - Journal of Partial Differential Equations
VL - 1
SP - 31
EP - 41
PY - 1988
DA - 1988/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5850.html
KW - 
AB -  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).