Admissibility and Observability of Observation Operators for Semilinear Problems

作者：Baroun Mahmoud^*; Jacob Birgit

来源：Integral Equations and Operator Theory, 2009, 64(1): 1-20.

DOI：10.1007/s00020-009-1675-0

• Admissible observation operators
• exact observability
• Lebesgue extension
• nonlinear semigroup
• semilinear problems

This paper deals with semilinear evolution equations with unbounded observation operators. Sufficient conditions are given guaranteeing that the output function of a semilinear system is in L(loc)(2)([0, infinity);Y). We prove that the Lebesgue extension of the observation operators are invariant under non-linear globally Lipschitz continuous perturbations. Further, relations between the corresponding Lambda-extensions are studied. We show that exact observability of linear autonomous system is conserved under small Lipschitz perturbations. The obtained results are illustrated by several examples.

• 出版日期2009-5