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

Marcelo M Cavalcanti , Pierre Cornilleau , Valéria N. Domingos Cavalcanti , Luc Robbiano (1) , Valéria N Domingos Cavalcanti

1 LMV - Laboratoire de Mathématiques de Versailles

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.

Mots clés: 2010 Mathematics Subject Classification: 35L05; 35l20; 35B40 Wave equation; Zaremba boundary conditions; microlocal analysis

Domaines: Equations aux dérivées partielles [math.AP]

Marcelo M Cavalcanti, Pierre Cornilleau, Valéria N. Domingos Cavalcanti, Luc Robbiano, Valéria N Domingos Cavalcanti. Semi-classical defect measure and internal stabilization for the semilinear wave equation subject to Zaremba boundary conditions. 2021. ⟨hal-03394819⟩