Abstract
This chapter explains the Fuchsian type partial differential equations. In analytic function spaces, the unique solvability is proved by Hasegawa, Baouendi–Goulaouic, and Tahara. The local solvability or the well-posedness of the Cauchy problem is in C∞ function spaces in Gevrey function spaces in hyperfunction spaces and in distribution spaces. The local solvability is proved in hyperfunction spaces for elliptic equations and by in distribution spaces for second-order equations of various types.
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