Logarithmic decay of hyperbolic equations with arbitrary boundary damping
Xiaoyu Fu
TL;DR
This paper establishes logarithmic stability for hyperbolic equations with arbitrary boundary damping using Carleman estimates, without restrictions on the observation boundary, advancing understanding of boundary control and stability.
Contribution
It introduces a novel approach to prove logarithmic stability for hyperbolic equations with arbitrary boundary observation, removing previous boundary restrictions.
Findings
Logarithmic stability estimate for hyperbolic equations established
Resolvent operator estimate derived using Carleman estimates
Stability proven without assumptions on observation subboundary
Abstract
In this paper, we study the logarithmic stability for the hyperbolic equations by arbitrary boundary observation. Based on Carleman estimate, we first prove an estimate of the resolvent operator of such equation. Then we prove the logarithmic stability estimate for the hyperbolic equations without any assumption on an observation subboundary.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering · Advanced Mathematical Physics Problems