Differential inclusions governed by non convex perturbations of \(m\)- accretive operators (Q1174380)

The authors consider the problem \(u'\in-Au(t)+Ft,u(t)\), \(u(0)=u_ 0\), where \(A:D(A)\subset X\to 2^ X\) is an \(m\)-accretive operator such that \(-A\) generates a compact semigroup (\(X\) is a separable Banach space), \(F:[0,T]\times \overline{D(A)}\to 2^ X\) is a closed-valued, lower semicontinuous map. They prove the existence of integral solutions, and if \(F(t,u)\) is also bounded by \(g_ 1(t)\| u\|+g_ 2(t)\), where \(g_ 1\), \(g_ 2\) are integrable, they show that all mild solutions are defined on all of \([0,T]\). This result is applied to nonlinear parabolic PDE.