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

  • J. Apraiz [1]
    1. [1] Universidad del País Vasco/Euskal Herriko Unibertsitatea

      Universidad del País Vasco/Euskal Herriko Unibertsitatea

      Leioa, España

  • Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 2, Nº. 2, 2017, págs. 543-558
  • Idioma: inglés
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • 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.


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