Asymptotics of the critical non-linear wave equation for a class of non star-shaped obstacles

2012/06/01 by Farah Abou Shakra, Shakra, Farah Abou · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1206.0272

corrected typos and updated references, to appear in JHDE, arXiv admin note: text overlap with arXiv:0805.4733 by other authors

arxiv created 2013/05/15 · arxiv updated 2013/05/17

Abstract

Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering for a class of non star-shaped obstacles called illuminated from exterior. The main tool we use is the method of multipliers with weights that generalize the Morawetz multiplier to suit the geometry of the obstacle.

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