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

Julien Royer (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We study the high frequency limit for the dissipative Helmholtz equation when the source term concentrates on a submanifold of R^n. 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.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Julien Royer. Semiclassical measure for the solution of the Helmholtz equation with an unbounded source. Asymptotic Analysis, 2015, 91. ⟨hal-00784668⟩