**J. Gvazava and S. Kharibegashvili**

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

**abstract:**

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.