Nonlocal Regularization of Protter-Morawetz BVP for the 3-D Tricomi equation

This is a work in progress with my coauthor Barbara Keyfitz, Professor of Mathematics in Ohio State University. In this paper some boundary-value problems (BVPs) for partial differential equations are discussed. The situation is rather surprising and there is no general understanding even more than sixty years after Murray Protter (Berkeley) formulated them. These are multidimensional analogues of classical BVPs on the plane and intuitively the initial expectations was that their properties would be similar. Unexpectedly, it turned out that unlike the two-dimensional variants, the Protter problems are not well-posed. The generalized solution is uniquely determined, but it may have a strong singularity at an isolated boundary point even for the wave equation with infinitely smooth right-hand side. In this paper will be introduced a new BVP which will be nonlocal and in some sence is a "regularizer" for the probably strongly overdetermined original Protter-Morawetz problem for the 3-D Tricomi equation. Let note also that we put a long list of bibliography inside.