Nonlinear transmission problem with a dissipative boundary condition of memory type
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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.
CitationAndrade, D., Fatori, L. H., & Muñoz Rivera, J. E. (2006). Nonlinear transmission problem with a dissipative boundary condition of memory type. Electronic Journal of Differential Equations, 2006(53), pp. 1-16.
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