Semilinear observation systems

Baroun, Mahmoud
Jacob, Birgit
Maniar, Lahcen
Schnaubelt, Roland

facul_10; 09

Date: 15. 09. 2010
Abstract:
In this paper, we introduce locally Lipschitz observation systems for nonlinear semigroups and show that they can be represented by an `admissible' nonlinear output operator defined on a suitable subspace. In the semilinear case, this concept fits well to the Lebesgue extension known from linear system theory. Also in the semilinear case, we show robustness of exact observability near equilibria under locally small Lipschitz perturbations. Finally, we apply our results to a damped nonlinear beam equation and a semilinear thermo-elastic system.

Primary MSC: 93C10 Nonlinear systems
Secondary MSC: 34G10 Linear equations [See also 47D06, 47D09] , 20M20 Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15] , 93B07 Observability , 93B18 Linearizations , 49J27 Problems in abstract spaces [See also 90C48, 93C25]