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

Article type: Research Article

Authors: Royer, Julien

Affiliations: Institut de Mathématiques de Toulouse, 118, Route de Narbonne, 31062 Toulouse Cédex 9, France. E-mail: [email protected]

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.

Keywords: non-selfadjoint operators, resolvent estimates, Helmholtz equation, semiclassical measures

DOI: 10.3233/ASY-141255

Journal: Asymptotic Analysis, vol. 91, no. 1, pp. 11-32, 2015