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2019 | OriginalPaper | Chapter

Applications of Observability Inequalities

Author : Jone Apraiz

Published in: Recent Advances in Differential Equations and Applications

Publisher: Springer International Publishing

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Abstract

This article presents two observability inequalities for the heat equation over Ω × (0, T). In the first one, the observation is from a subset of positive measure in Ω × (0, T), while in the second, the observation is from a subset of positive surface measure on ∂Ω × (0, T). We will provide some applications for the above-mentioned observability inequalities, the bang-bang property for the minimal time control problems and the bang-bang property for the minimal norm control problems, and also establish new open problems related to observability inequalities and the aforementioned applications.

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next chapter Optimal Design of Piezoelectric Microactuators: Linear vs Non-linear Modeling
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Metadata
Title
Applications of Observability Inequalities
Author
Jone Apraiz
Copyright Year
2019
Book
Recent Advances in Differential Equations and Applications

Print ISBN: 978-3-030-00340-1

Electronic ISBN: 978-3-030-00341-8

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-00341-8_1

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