Asymptotic Behaviors of Global Solutions to Fourth-order Parabolic and Hyperbolic Equations with Dirichlet Boundary Conditions
Abstract
This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations with Dirichlet boundary conditions. The equations model Micro-Electro-Mechanical Systems (MEMS) and are depending on a positive voltage parameter λ. We establish the convergence of global solutions to an equilibrium, along with the convergence rate estimates. Supporting numerical simulations are presented.
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