Applications of Observability Inequalities

  • Jone ApraizEmail author
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 18)


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.


Parabolic equations Control theory Controllability Observability inequalities Bang-Bang properties 

AMS 2010 Codes:

49J20 49J30 58E25 93B05 93B07 35K05 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad del País VascoLeioaSpain

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