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 u ̇ ( t ) + A ( t ) u ( t ) ∋ 0 , t ≥ s , u ( s ) = u 0 , where A ( t ) is a family of nonlinear multivalued γ -accretive operators with D ( A ( t ) ) possibly depending on t .