An observability for parabolic equations from a measurable set in time

2011/09/18 by Kim Dang Phung, Phung, Kim Dang, Gengsheng Wang +1 · 4 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Electrical engineering #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1109.3863

openalex publication_date 2011/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a new observability estimate for parabolic equations in Ω×(0,T), where Ω is a convex domain. The observation region is restricted over a product set of an open nonempty subset of Ω and a subset of positive measure in (0,T). 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.

Cited by

• Global controllability of the Cahn-Hilliard equation
• Fractal Remez inequality on the sphere and observability of the heat equation
• Resolvent bounds imply observability from measurable time sets for Schrödinger equations
• Null controllability of the 1D heat equation with interior inverse square potential

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