Generalized solutions to Protter problems for 3-D Keldysh type equations

Some three-dimensional boundary value problems for equations of Keldysh type are studied. Such type problems, but for equations of Tricomi type are stated by M. H. Protter [25] as 3-D analogues of Darboux or Cauchy-Goursat plane problems. It is well known that in contrast of well-posedness of 2D problems, the Protter problems are strongly ill-posed. In [12] Protter problem for Keldysh type equations is formulated and it is shown that it is not correctly set since the homogeneous adjoint problem has infinitely many nontrivial classical solutions. In the present paper a notion for generalized solution to Protter problem for Keldysh type equations is introduced. Further, results for existence and uniqueness of such solution are obtained.