<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

Publié en ligne: 15 déc. 2017

Pages: 543 - 558

Reçu: 01 juin 2017

Accepté: 15 déc. 2017

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

Mots clés
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

Publié en ligne: 15 déc. 2017

Pages: 543 - 558

Reçu: 01 juin 2017

Accepté: 15 déc. 2017

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

Mots clésParabolic 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.

Mots clés
Parabolic equations, control theory, controllability, observability inequalities, Bang-Bang properties