Regresar

Approximate controllability of discrete semilinear systems and applications

Abstract:

In this paper we study the approximate controllability of the following semilinear difference equation z(n + 1) = A(n)z(n) + B(n)u(n) + f(n, z(n), u(n)), n ϵ N∗, z(n) ϵ Z, u(n) ϵ U, where Z, U are Hilbert spaces, A ϵ l∞(N, L(Z)), B ϵ l∞(N, L(U, Z)), u ϵ l (N, U) and the nonlinear term f: N × Z × U → Z is a suitable function. We prove that, under some conditions on the nonlinear term f, the approximate controllability of the linear equation is preserved. Finally, we apply this result to a discrete version of the semilinear wave equation.