On the Goursat problem in the Gevrey class for some second order equations

Abstract

The Goursat problem for certain types of second order linear equations is considered. The Goursat problem for those second order equations is not $\mathcal{E}$-wellposed in general. For a certain type homogeneous equations, the Goursat problem is $\mathcal{E}$-wellposed. Necessary or sufficient conditions on lower order terms for $\mathcal{E}$-wellposedness are given. Wellposedness in Gevrey class is discussed.