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arXiv · 2110.12689

Semi-classical defect measure and internal stabilization for the semilinear wave equation subject to Zarembaboundary conditions

Marcelo Cavalcanti·Pierre Cornilleau·Valéria Domingos Cavalcanti·Luc Robbiano·Valéria Cavalcanti
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Abstract

In this article we exploite the uniform decay for damped linear wave equation with Zaremba boundary condition, obtained in a previous work, to treat the same problem in nonlinear context. We need a uniqueness assumption, usual for this type of nonlinear problem. The result is deduced from an observation estimate for nonlinear problem proved by a contradiction argument.

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Marcelo Cavalcanti, Pierre Cornilleau, Valéria Domingos Cavalcanti, Luc Robbiano, Valéria Cavalcanti. 2021-10-25. Semi-classical defect measure and internal stabilization for the semilinear wave equation subject to Zarembaboundary conditions. https://arxiv.org/abs/2110.12689

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