Article
Observability Inequalities for Parabolic Equations over Measurable Sets and Some Applications Related to the Bang-Bang Property for Control Problems
Authors
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.
Keywords
Parabolic equations, control theory, controllability, observability inequalities, Bang-Bang properties, 49J20, 49J30, 58E25, 93B05, 93B07, 35K05
Citation
Apraiz, J. (2017). 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, 2(2), 543–558. https://doi.org/10.21042/AMNS.2017.2.00045
J. Apraiz, “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, vol. 2, no. 2, pp. 543–558, 2017, doi: 10.21042/AMNS.2017.2.00045.
Apraiz J. 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. 2017;2(2):543–558. doi:10.21042/AMNS.2017.2.00045.
Apraiz, J. (2017), ‘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, 2(2), pp. 543–558. Available at: https://doi.org/10.21042/AMNS.2017.2.00045.
Apraiz, J. “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, vol. 2, no. 2, 2017, pp. 543–558. https://doi.org/10.21042/AMNS.2017.2.00045.
Apraiz, J. “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 2, no. 2 (2017): 543–558. https://doi.org/10.21042/AMNS.2017.2.00045.
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Published by: Engineering Journals
