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 L2loc([0, ∞); Y). We prove that the Lebesgue extension of the observation operators are invariant under nonlinear globally Lipschitz continuous perturbations. Further, relations between the corresponding Ùbigwedge-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.
展开▼
机译：本文研究了带有无界观测算子的半线性发展方程。给出了充分的条件，以保证半线性系统的输出函数在L 2 loc （[0，∞];是的。我们证明了观测算子的Lebesgue扩展在非线性全局Lipschitz连续扰动下是不变的。此外，研究了相应的“ bigwedge”扩展名之间的关系。我们证明了线性自主系统的精确可观性在小的Lipschitz扰动下是守恒的。几个例子说明了获得的结果。
展开▼
