Nonlinear Volterra Integrodifferential Equations

Using Bessel potential spaces and interpolation theory, we show the existence and uniqueness of global weak solutions of the semilinear Volterra integrodifferential equation u′(t) + Au(t) = ∫t0a(t, s)g(s, u(s)) ds + ƒ(t, u(t)), t ≥ 0u(0) = u0. The operator A is the negative infinitesimal generator of an analytic semigroup in a Banach space X and g(t, n) is the realization in X of an arbitrary polynomial differential operator in divergence form having the same order as A.