Exact controllability for semilinear difference equation and application
Titel:
Exact controllability for semilinear difference equation and application
Auteur:
Leiva, Hugo Uzcategui, Jahnett
Verschenen in:
Journal of difference equations and applications
Paginering:
Jaargang 14 (2008) nr. 7 pagina's 671-679
Jaar:
2008-07
Inhoud:
In this paper, we study the exact controllability of the following semilinear difference equation[image omitted] z(n) ∈ Z, u(n) ∈ U, where Z, U are Hilbert spaces, [image omitted] , [image omitted] , [image omitted] , [image omitted] and the nonlinear term f : Z × U → Z satisfies:[image omitted] We prove the following statement: If the linear equation is exactly controllable and L < < 1, then the nonlinear equation is also exactly controllable. That it to say, the controllability of the linear equation is preserved under nonlinear perturbation f (z,u). Finally, we apply this result to a discrete version of the semilinear heat equation.
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