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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Apraiz, J. (2019). Applications of Observability Inequalities. In: García Guirao, J., Murillo Hernández, J., Periago Esparza, F. (eds) Recent Advances in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-030-00341-8_1
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DOI: https://doi.org/10.1007/978-3-030-00341-8_1
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