Semiclassical measure for the solution of the Helmholtz equation with an unbounded source

2013/02/04 by Julien Royer, Royer, Julien
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1302.0811

arxiv created 2013/02/04 · openalex publication_date 2013/02/04 · arxiv updated 2013/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the high frequency limit for the dissipative Helmholtz equation when the source term concentrates on a submanifold of Rⁿ. We prove that the solution has a unique semi-classical measure, which is precisely described in terms of the classical properties of the problem. This result is already known when the micro-support of the source is bounded, we now consider the general case.

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