Existence and flow invariance of solutions to non-autonomous Cauchy problems under separate subtangential conditions

We investigate the problem of existence and flow invariance of mild solutions to the non-autonomous Cauchy problem u̇(t)+A(t)u(t)∋0, t≥s, u(s)=u0, where A(t) is a family of nonlinear multivalued γ-accretive operators with D(A(t)) possibly depending on t.