The damped elastic stretched string equation generalized: existence, uniqueness, regularity and stability

In this paper we prove existence for all time t≦0, uniqueness, regularity and stability of solutions of a Cauchy problem in a Hilbert space H for the equation when δ is a positive constant sufficiently large, A an operator in H and M a given function, satisfying convenient hypothesis. An application is given; in particular, existence for all t≦0, uniqueness and stability of classical solutions of an initial-boundary value problem for the nonlinear partial integro-differential equation (βk positive constants) is obtained. AMOS(MOS) No. 35L20; 35B40