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

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  • Dedicated to Professor Norio Shimakura on the occasion of his sixtieth birthday

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Abstract

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

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