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Abstract: We study the semiclassical measures for the solution of a dissipativeHelmholtz equation with a source term concentrated on a bounded submanifold.The potential is not assumed to be non-trapping, but trapped trajectories haveto go through the region where the absorption coefficient is positive. In thatcase, the solution is microlocally written around any point away from thesource as a sum finite or infinite of lagragian distributions. Moreover weprove and use the fact that the outgoing solution of the dissipative Helmholtzequation is microlocally zero in the incoming region.



Author: Julien Royer LMJL

Source: https://arxiv.org/



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