NONLINEAR VOLTERRA INTEGRODIFFERENTIAL EQUATIONS

[摘要] 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) = integral(0)(t) a(t,s)g(s,u(s)) ds + f(t,u(t)), t greater than or equal to 0 u(0) = u(0). 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. (C) 1994 Academic Press, Inc.

[发布日期] 1994-12-01