The Gevrey boundary value problems for mixed type equations

摘要

The Gevrey boundary value problems are studied for mixed type equations. We rely on the theory of integral equations with the Cauchy kernel. As is known, the Holder classes of solutions to forward-backward parabolic equations essentially depend on gluing conditions and a noninteger Holder exponent of the space. The unique solvability of the Gevrey boundary value problems for equations of the second and third orders is proven.