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Available online: December 15, 2017

Observability Inequalities for Parabolic Equations over Measurable Sets and Some Applications Related to the Bang-Bang Property for Control Problems

J. Apraiz
Volume 2 - Issue 2.     Year 2017.     Pages 543–558.

DOI: 10.21042/AMNS.2017.2.00045

Abstract

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

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ISSN:
2444-8656
Category:
Applied Mathematics, Nonlinear Sciences

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