# Global existence and quenching for a damped hyperbolic MEMS equation with the fringing field

## DOI:

https://doi.org/10.5556/j.tkjm.48.2017.2136## Keywords:

MEMS, damped hyperbolic, fringing field, local solution, global solution, quenching## Abstract

We study a damped hyperbolic MEMS equation with the fringing field.It arises in the Micro-Electro Mechanical System(MEMS) devices. We give some criteria for global existence and quenching of the solution.First we establish a time-local solution by a contraction mapping theorem. This procedure is standard.Next we show that there exists a global solution for the small parameter and initial value. Finally, we deal with the quenching result for the large parameter.## References

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*Tamkang Journal of Mathematics*,

*48*(1), 31–47. https://doi.org/10.5556/j.tkjm.48.2017.2136