JournalsjemsVol. 15, No. 2pp. 681–703

An observability estimate for parabolic equations from a measurable set in time and its applications

  • Kim Dang Phung

    CNRS-Université d'Orléans, France
  • Gengsheng Wang

    Wuhan University, Wuhan, Hubei, China
An observability estimate for parabolic equations from a measurable set in time and its applications cover
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Abstract

This paper presents a new observability estimate for parabolic equations in Ω×(0,T)\Omega\times\left( 0,T\right) , where Ω\Omega is a convex domain. The observation region is restricted over a product set of an open nonempty subset of Ω\Omega and a subset of positive measure in (0,T)\left( 0,T\right) . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.

Cite this article

Kim Dang Phung, Gengsheng Wang, An observability estimate for parabolic equations from a measurable set in time and its applications. J. Eur. Math. Soc. 15 (2013), no. 2, pp. 681–703

DOI 10.4171/JEMS/371