Problems without initial conditions with integral restrictions for hyperbolic equations and systems on a line (Q801213)

The paper is concerned with solving a system of hyperbolic first order equations under integral constraints instead of initial conditions. The hyperbolic systems under consideration are linear, but have discontinuous coefficients. The main result here consists in finding the sufficient solvability conditions of the stated problem in the class of generalized solutions. The uniqueness of the latter is studied. The author received analogous results for systems of hyperbolic equations of arbitrary order. Sufficient conditions are given under which the generalized solution becomes the classical one.