Wave equation with Robin condition, quantitative estimates of strong\n unique continuation at the boundary

2016/03/29 by Eva Sincich, Sincich, Eva, Sergio Vessella +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1603.08778

openalex publication_date 2016/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result of the present paper consists in a quantitative estimate of\nunique continuation at the boundary for solutions to the wave equation. Such\nestimate is the sharp quantitative counterpart of the following strong unique\ncontinuation property: let u be a solution to the wave equation that\nsatisfies an homogeneous Robin condition on a portion S of the boundary and\nthe restriction of u_{\| S} on S is flat on a segment 0 \× J\nwith 0\∈ S then u_{\| S} vanishes in a neighborhood of 0 \× J.\n

Related

• Quantitative estimates of strong unique continuation for anisotropic wave equations
• Quantitative unique continuation for Robin boundary value problems on C^1,1 domains
• On the blowup of quantitative unique continuation estimates for waves and applications to stability estimates
• Unique continuation for water waves and dispersive multiplier equations
• Unique continuation for the wave equation: the stability landscape