Andrade, Doherty; Fatori, Luci Harue; Muñoz Rivera, Jaime E. Nonlinear transmission problem with a dissipative boundary condition of memory type. (English) Zbl 1112.35021 Electron. J. Differ. Equ. 2006, Paper No. 53, 16 p. (2006). Summary: We consider a differential equation that models a material consisting of two elastic components. One component is clamped while the other is in a viscoelastic fluid producing a dissipative mechanism on the boundary. So, we have a transmission problem with boundary damping condition of memory type. We prove the existence of a global solution and its uniformly decay to zero as time approaches infinity. More specifically, the solution decays exponentially provided the relaxation function decays exponentially. Cited in 20 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35L70 Second-order nonlinear hyperbolic equations 74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) 35L20 Initial-boundary value problems for second-order hyperbolic equations Keywords:wave equation; asymptotic behavior; memory; two elastic components; viscoelastic fluid; boundary damping condition PDFBibTeX XMLCite \textit{D. Andrade} et al., Electron. J. Differ. Equ. 2006, Paper No. 53, 16 p. (2006; Zbl 1112.35021) Full Text: EuDML EMIS