ON THE CHARACTERISTIC INITIAL-VALUE PROBLEM FOR LINEAR PARTIAL FUNCTIONAL-DIFFERENTIAL EQUATIONS OF HYPERBOLIC TYPE

Theorems on the Fredholm alternative and well-posedness of the characteristic initial-value problem partial derivative(2)u(t,x)/partial derivative t partial derivative x = l(u)(t,x) + q(t,x), u(t,c) = phi(t) for t is an element of [a,b], u(a,x) = psi(x) for x is an element of [c,d], are established, where l : C(D; R) -> L(D; R) is a linear bounded operator, q is an element of L(D; R), phi: [a, b] -> R, psi: [c,d] -> R are absolutely continuous functions and D = [a,b] x [c,d]. Some solvability conditions of the problem considered are also given.