Approximate controllability of neutral functional differential system with unbounded delay
The authors study the approximate controllability of neutral functional differential systems with unbounded delay of the form \[ {d\over dt}\{x(t)+F(t,x_t)\}=Ax(t)+G(t,x_t)+Bv(t), 0<t<T, x_0=\phi, \] where \(F,G: [0,T]\times {\mathcal B}\to X\) are continuous functions, \({\mathcal B}\) is an abstract phase space, \(A\) is the infinitesimal generator of an analytic semigroup of bounded linear operators on a Banach space \(X,\) the control function \(v(\cdot)\) is given in \(L^2(0,T:V),\) which is a Banach space of admissible control functions, with \(V\) as a Banach space. Finally, \(B\) is a bounded linear operator from \(L^2(0,T:V)\) into \(L^2(0,T:X).\) An example which illustrates the theoretical results is also presented.
scientific article; zbMATH DE number 1780261