On characterization and perturbation of local $C$-semigroups

Yuan-Chuan Li, Sen-Yen Shaw
2007 Proceedings of the American Mathematical Society  
Let S(·) be a (C 0 )-group with generator −B, and let {T (t); 0 ≤ t < τ} be a local C-semigroup commuting with S(·). Then the operators It is proved that if C is injective and A is the generator of T (·), then A + B is closable and A + B is the generator of V (·). Also proved are a characterization theorem for local C-semigroups with C not necessarily injective and a theorem about solvability of the abstract inhomogeneous Cauchy problem: u (t) = Au(t) + Cf (t), 0 < t < τ; u(0) = Cx.
doi:10.1090/s0002-9939-06-08549-2 fatcat:rqq4lkuqcjfbrc3snwm76ymgsm