2013/05/28 by Ambroise Vest, Vest, Ambroise
Engineering · Mathematics · Physics and Astronomy · #35L05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Dynamics and Fractals #Optimization and Control (math.OC) #Primary 93B07 #Quantum chaos and dynamical systems #Secondary 42C99 #Stability and Controllability of Differential Equations
paper · doi:10.48550/arxiv.1305.6461
openalex publication_date 2013/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper by A. Szijártó and J. Hegedűs in which the authors ask the question of determining the initial data by only knowing the position of the string at two distinct time instants. The choice of the observation instants is crucial and the estimations rely on the Fourier series expansion of the solutions and results of Diophantine approximation.