Stability of observations of partial differential equations under uncertain perturbations. (English) Zbl 1396.93030
Summary: We demonstrate the stability of observability estimates for solutions to wave and Schrödinger equations subjected to additive perturbations. This work generalizes recent averaged observability/control results by allowing for systems consisting of operators of different types. We also consider the simultaneous observability problem by which one tries to estimate the energy of each component of a system under consideration. Our analysis relies on micro-local defect tools, in particular on standard \(H\)-measures when the main system dynamic is governed by the wave operator, and parabolic \(H\)-measures in the case of the Schrödinger operator.
MSC:
| 93B07 | Observability |
| 93B05 | Controllability |
| 93C20 | Control/observation systems governed by partial differential equations |
| 93D09 | Robust stability |
| 35J10 | Schrödinger operator, Schrödinger equation |
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