Observability inequality, the interpolation inequality and the spectral inequality for the degenerate parabolic equation in R

2023/06/15 by Yuanhang Liu, Liu, Yuanhang, Weijia Wu +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2306.08884

openalex publication_date 2023/06/15 · openalex created_date 2023/06/17 · openalex updated_date 2026/07/28

Abstract

This paper investigates the interrelationships between the observability inequality, the Hölder-type interpolation inequality, and the spectral inequality for the degenerate parabolic equation in ℝ. We elucidate the distinctive properties of observable sets pertaining to the degenerate parabolic equation. Specifically, we establish that a measurable set in ℝ fulfills the observability inequality when it exhibits γ-thickness at a scale L, where γ>0 and L>0.

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