Nonlocal Boundary Value Problems for Linear Hyperbolic Systems

Abstract

Boundary value problems in a characteristic rectangle Ω = [0, ω1]×[0, ω2] for second order linear hyperbolic systems are considered. For initial–boundary value problems there are established: (i) Necessary and sufficient conditions of well–posedness; (ii) Necessary conditions of solvability; (iii) Effective sufficient conditions of solvability of two–point initial–boundary value problems; (iv) Effective sufficient conditions of solvability of initial–periodic problems; (v) Necessary and sufficient conditions of solvability of ill–posed initial–boundary value problems; (vi) Necessary and sufficient conditions of solvability of ill–posed initial–periodic problems. For nonlocal boundary value problems there are established: (i) Necessary and sufficient conditions of well–posedness; (ii) Necessary conditions of solvability; (iii) Effective sufficient conditions of solvability of problems with Nicoletti type boundary conditions; (iv) Effective sufficient conditions of solvability of problems with boundary conditions of periodic type ; (iv) Effective sufficient conditions of solvability of doubly–periodic problems; (v) Necessary and sufficient conditions of solvability of ill–posed doubly–periodic problems.