Solutions of Evolution Equations in Hilbert Space

Equation (1) is linear when g is independent of U. We refer to Pazy [9] and Tanabe [lo] for linear evolution equations with the operators A(t) assumed to be infinitesimal generators of C,-semigroups. A strong solution u of (1) requires u(t) E g(A(t)) for each t. It is possible that there are no strong solutions, but solutions of weaker types exist which do not need the abovementioned requirement (see [9, lo] in the