On the admissibility of observation operators for evolution families. (English) Zbl 1514.34105
In the paper under review, the author considers the unbounded observation operators for non-autonomous evolution equations of first order. The corresponding operator family \((A(t))_{t\in [0,\tau]}\) under the consideration of the author satisfies the relative \(p\)-Dini condition and each single operator \(A(t)\) has maximal regularity. Under these assumptions, there exists an evolution system associated with the family \((A(t))_{t\in [0,\tau]}\). The main results of paper are obtained by assuming that the operator family \((A(t))_{t\in [0,\tau]}\) is Hölder continuous or Lipschitz continuous.
Reviewer: Marko Kostić (Novi Sad)
MSC:
| 34G10 | Linear differential equations in abstract spaces |
| 37C60 | Nonautonomous smooth dynamical systems |
Keywords:
evolution equations; admissible observation; \(L^p\)-maximal regularity; non-autonomous; evolution families; Banach spaceReferences:
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