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
• DOI: 10.21042/amns.2017.2.00045
• 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.