J. Gvazava and S. Kharibegashvili

To The Theory of Boundary Value Problems for Hyperbolic Type Equations and Systems

Most well--posed boundary value problems, if considered in spaces of higher dimension, have a lot of different variants which, unlike the original problems, do not obey the standard existence and uniqueness conditions. This observation is, in particular, typical of equations and systems of hyperbolic type. Just such problems are needed to be investigated for the purpose of applications. A. V. Bitsadze obtained a number of results in this direction both for strictly hyperbolic and degenerating linear and nonlinear equations. In the subsequent years, these results stimulated investigations of his followers. Some of the results are discussed in the paper.

Mathematics Subject Classification: 35L20, 35L80.

Key words and phrases: Hyperbolic equations and systems, nonlinear equations and systems, problems of Goursat and Darboux type, characteristic problem, multidimensional analogues of Goursat and Darboux type problems.