Observability Inequalities and Measurable Sets

By Jone Apraiz, Luis Escauriaza, G. Wang, C. Zhang. 2012

162 citations recorded by the source corpus.

This paper presents two observability inequalities for the heat equation over $\Omega\times(0,T)$. In the first one, the observation is from a subset of positive measure in $\Omega\times(0,T)$, while in the second, the observation is from a subset of positive surface measure in $\partial\Omega \times(0,T)$. It also proves the Lebeau-Robbiano spectral inequality when $\Omega$ is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/7a1776e84f124d437ab97748ffc2068565ef31c4

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Null-controllability of hypoelliptic quadratic differential equations (2016, unknown): “3) from a telescopic serie argument due to [47] (see also [48]) and already exploited in [2, 52, 63].”
Observable set, observability, interpolation inequality and spectral inequality for the heat equation in Rn (2017, methodology): “It is an analogy result for solutions of the heat equation in a bounded domain with an analytic boundary (see [2, 16]).”
Optimal Shape and Location of Sensors for Parabolic Equations with Random Initial Data (2014, background): “E φj(x) 2 dx > e−2C √ μj C2|E| , (82) valid uniformly over measurable sets E, proved in [5] and extending previous results in [39] on open sets.”