Stabilization of the wave equation with variable coefficients and boundary condition of memory type

Article type: Research Article

Authors: Nicaise, Serge | Pignotti, Cristina

Affiliations: Université de Valenciennes et du Hainaut Cambrésis, MACS, Institut des Sciences et Techniques de Valenciennes, 59313 Valenciennes cedex 9, France E-mail: snicaise@univ-valenciennes.fr | Dipartimento di Matematica Pura e Applicata, Università di L'Aquila, Via Vetoio, Loc. Coppito, 67010 L'Aquila, Italy E-mail: pignotti@univaq.it

Abstract: We consider the stabilization of the wave equation with space variable coefficients in a bounded region with a smooth boundary, subject to Dirichlet boundary conditions on one part of the boundary and linear or nonlinear dissipative boundary conditions of memory type on the remainder part of the boundary. Our stabilization results are mainly based on the use of differential geometry arguments, on the multiplier method and the introduction of suitable Lyapounov functionals.

Keywords: wave equation, variable coefficients, memory boundary conditions, stabilization

Journal: Asymptotic Analysis, vol. 50, no. 1-2, pp. 31-67, 2006