Energy decay for solutions of the wave equation with general memory boundary conditions.

Pierre Cornilleau (1) , Serge Nicaise (2)

1 ICJ - Institut Camille Jordan
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

We consider the wave equation in a smooth domain subject to Dirichlet boundary conditions on one part of the boundary and dissipative boundary conditions of memory-delay type on the remainder part of the boundary, where a general borelian measure isinvolved. Under quite weak assumptions on this measure, using the multiplier method and a standard integral inequality we show the exponential stability of the system. Some examples of measures satisfying our hypotheses are given, recovering and extending some of the results from the literature.

Mots clés: stabilization; wave equation; delay equation

Domaines: Optimisation et contrôle [math.OC]

Pierre Cornilleau, Serge Nicaise. Energy decay for solutions of the wave equation with general memory boundary conditions.. 2009. ⟨hal-00360382⟩