If A: D(A) X→X is a densely defined and closed linear operator, which generates a linear semigroup S (t) in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems: u' (t...If A: D(A) X→X is a densely defined and closed linear operator, which generates a linear semigroup S (t) in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems: u' (t) = Au (t) + Bx( t) + f( t, u(t) ), 0≤t ≤ T with nonlocal initial condition u(0) = u0 + g(u) is discussed in Banach space X. The results show that if semigroup S(t) is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S(t) is compact or strongly continuous. For illustration, a partial differential equation is worked out.展开更多
基金the National Natural Science Foundation of China(No.10674024)
文摘If A: D(A) X→X is a densely defined and closed linear operator, which generates a linear semigroup S (t) in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems: u' (t) = Au (t) + Bx( t) + f( t, u(t) ), 0≤t ≤ T with nonlocal initial condition u(0) = u0 + g(u) is discussed in Banach space X. The results show that if semigroup S(t) is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S(t) is compact or strongly continuous. For illustration, a partial differential equation is worked out.