Energy Decay Rate for the Kelvin-Voigt Type Wave Equation With Balakrishnan-Taylor Damping and Acoustic Boundary

Abstract

Abstract. In this paper, we study exponential stabilization of the vibrations of the Kelvin-Voigt type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in R n . To stabilize the systems, we incorporate separately, the internal material damping in the model as like Kang [3]. Energy decay rate are obtained by the exponential stability of solutions by using multiplier technique.

A global nonexistence of solutions for a quasilinear viscoelastic wave equation with acoustic boundary conditions

“…Boukhatem and Benabderrahmane [2,3] studied the existence, blow-up, and decay of solutions for viscoelastic wave equations with acoustic boundary conditions. Recently, many authors have treated wave/beam equations with acoustic boundary conditions, see [7,8,10,12,13,15,16] and the references therein. Graber and Haid-Houari [5] studied the blow-up solutions for a nonlinear wave equation with porous acoustic boundary conditions:…”