<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This article presents two observability inequalities for the heat equation over Ω× (0,<italic>T</italic>). In the first one, the observation is from a subset of positive measure in Ω× (0,<italic>T</italic>), while in the second, the observation is from a subset of positive surface measure on ∂Ω× (0,<italic>T</italic>). 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.</p></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, time optimal and minimal norm control problems, and also establish new open problems related to observability inequalities and the aforementioned applications.

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

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

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

Published Online: Dec 15, 2017

Page range: 543 - 558

Received: Jun 01, 2017

Accepted: Dec 15, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00045

Keywords
Parabolic equations, control theory, controllability, observability inequalities, Bang-Bang properties

© 2017 J. Apraiz, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Dec 15, 2017

Page range: 543 - 558

Received: Jun 01, 2017

Accepted: Dec 15, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00045

KeywordsParabolic equations, control theory, controllability, observability inequalities, Bang-Bang properties

© 2017 J. Apraiz, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Parabolic equations, control theory, controllability, observability inequalities, Bang-Bang properties