caa a22 4500 606166009 CHVBK 20210128100656.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10440-014-9962-4 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9962-4 Kohlmann Martin Goerdelerstraße 36, 38228, Salzgitter, Germany aut The Abstract Quasilinear Cauchy Problem for a MEMS Model with Two Free Boundaries [Elektronische Daten] [Martin Kohlmann] In this paper, we reformulate a mathematical model for the dynamics of an idealized electrostatically actuated MEMS device with two elastic membranes as an initial value problem for an abstract quasilinear evolution equation. Applying the Contraction Mapping Theorem, it is shown that the model is locally well-posed in time for any value of the source voltage of the device. In addition it is proven that the MEMS model considered here possesses global solutions for small source voltages whereas for large source voltages solutions of the model have a finite maximal existence time. Furthermore, we comment on the relationship of our model to its stationary version and to its small aspect ratio limit by showing that there exists a unique exponentially stable steady state and by proving convergence towards a solution of the narrow gap model in the vanishing aspect ratio limit. Our results extend the discussion of the elliptic-parabolic MEMS model presented in Kohlmann (2014) leading to a Cauchy problem for a semilinear abstract evolution equation. Springer Science+Business Media Dordrecht, 2014 MEMS nationallicence Free boundary problem nationallicence Local and global well-posedness nationallicence Non-existence nationallicence Asymptotic stability nationallicence Small aspect ratio limit nationallicence Acta Applicandae Mathematicae Springer Netherlands 138/1(2015-08-01), 171-197 0167-8019 138:1<171 2015 138 10440 https://doi.org/10.1007/s10440-014-9962-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9962-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kohlmann Martin Goerdelerstraße 36, 38228, Salzgitter, Germany aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 138/1(2015-08-01), 171-197 0167-8019 138:1<171 2015 138 10440