Nonautonomous integro-differential equations of hyperbolic type
This paper concerns the following nonautonomous integro-differential equation in a Banach space \(X\): \(u'(t) = A(t) u(t) + \int^t_0 B(t,s) u(s) ds + f(t)\), \(t \in [0,T]\); \(u(0) = u_0\). The authors study existence and uniqueness of classical solutions without assuming that the common domain of \(A(t)\) is dense in \(X\), and the regularity problem in case the common domain of \(A(t)\) is dense in \(X\).
nonautonomous integro-differential equation
scientific article; zbMATH DE number 775650