Strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions
july, 2011
Type de publication :
Article (revues avec comité de lecture)
Journal :
Nonlinear Analysis: Theory, Methods & Applications, vol. 74, pp. 3137-3148
Lien externe :
DOI :
HAL :
Mots clés :
Wave equation; Acoustic semilinear boundary conditions; Interface; Structural acoustic model; Boundary stabilization; Strong stability; Decay rates
Résumé :
We consider a wave equation with semilinear porous acoustic boundary conditions. This is a coupled system of second and first order in time partial differential equations, with possibly semilinear boundary conditions on the interface. The results obtained are (i) strong stability for the linear model, (ii) exponential decay rates for the energy of the linear model, and (iii) local exponential decay rates for the energy of the semilinear model. This work builds on a previous result showing generation of a well-posed dynamical system. The main tools used in the proofs are (i) the Stability Theorem of Arendt–Batty, (ii) energy methods used in the study of a wave equation with boundary damping, and (iii) an abstract result of I. Lasiecka applicable to hyperbolic-like systems with nonlinearly perturbed boundary conditions.
BibTeX :
@article{Gra-2011,
author={Philip Jameson Graber },
title={Strong stability and uniform decay of solutions to a wave
equation with semilinear porous acoustic boundary conditions },
doi={10.1016/j.na.2011.01.029 },
journal={Nonlinear Analysis: Theory, Methods & Applications },
year={2011 },
month={7},
volume={74 },
pages={3137--3148},
}