This paper deals with Protter problems for Keldysh type equations in ℝ4. Originally such type problems are formulated by M. Protter for equations of Tricomi type. Now it is well known that Protter problems for mixed type equations of the first kind are ill-posed and for smooth right-hand side functions they have singular generalized solutions. In the present paper Protter problem for equations of second kind (Keldysh type) is formulated and it is shown that in the frame of classical solvability this problem is not well posed. Further, a notion for a generalized solution in suitable functional space is given. Results for existence and uniqueness of generalized solution of the considered problem are obtained. Some a priori estimates are stated.
Topics
Function space
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