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Viscosity dominated limit of global solutions to a hyperbolic equation in MEMS

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  • We study the asymptotic relation of solutions between the hyperbolic equation and the parabolic one over a one-dimensional bounded interval, both of which model a simple electrostatic micro-electro-mechanical system (MEMS) device. The relation is characterized by a limit as a physical parameter representing the strength of inertial forces tends to zero. We call this limit the viscosity dominated limit. It is shown that in this singular limit the solution of the hyperbolic model converges to that of the parabolic one globally in time. Also the higher order terms including the initial layer corrections, as well as the related error estimates, are derived. Furthermore, it is proved that the convergence is valid for global solutions with large initial data.
    Mathematics Subject Classification: Primary: 35B25, 35A01; Secondary: 35L20, 74H10.


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