S. Kharibegashvili
abstract:
In the present paper, for hyperbolic equations and
systems in angular domains, we consider the formulations of
problems representing natural continuation and further development
of the well-known classical formulations of Goursat and
Darboux type problems. For a wide class of linear normally hyperbolic
equations and systems of second order, the dependence of unique
solvability of the problems under consideration on the structure
of an angular domain as well as on the weighted space in which the
solution is sought, is established.
Some correct multidimensional analogues of Goursat and
Darboux type problems for hyperbolic equations are also considered.
Mathematics Subject Classification: 35L20.
Key words and phrases: Hyperbolic equations and systems, problems of Goursat and Darboux type, characteristic problem, multidimensional analogues of Goursat and Darboux type problems, angular domain, weighted space.