Spherical Logvinenko-Sereda-Kovrijkine type inequality and null-controllability of the heat equation on the sphere

2022/07/04 by Alexander Dicke, Dicke, Alexander, Ivan Veselić +1 · 1 citation
Computer Science · Engineering · Mathematics · #93B05 #93B07 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Primary 35Q93 #Secondary 35K05 #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2207.01369

openalex publication_date 2022/07/04 · openalex created_date 2022/07/07 · openalex updated_date 2026/07/28

Abstract

It is shown that the restriction of a polynomial to a sphere satisfies a Logvinenko-Sereda-Kovrijkine type inequality (a specific type of uncertainty relation). This implies a spectral inequality for the Laplace-Beltrami operator, which, in turn, yields observability and null-controllability with explicit estimates on the control costs for the spherical heat equation that are sharp in the large and in the small time regime.

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• Fractal Remez inequality on the sphere and observability of the heat equation

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