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A stochastic parabolic model of MEMS driven by fractional Brownian motion

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Abstract

In this paper, we study a stochastic parabolic problem that emerges in the modeling and control of an electrically actuated MEMS (micro-electro-mechanical system) device. The dynamics under consideration are driven by an one dimensional fractional Brownian motion with Hurst index \(H>1/2\). We derive conditions under which the resulting SPDE has a global in time solution, and we provide analytic estimates for certain statistics of interest, such as quenching times and the corresponding quenching probabilities. Our results demonstrate the non-trivial impact of the fractional noise on the dynamics of the system. Given the significance of MEMS devices in biomedical applications, such as drug delivery and diagnostics, our results provide valuable insights into the reliability of these devices in the presence of positively correlated noise.

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Acknowledgements

The research of A.M. is partially supported by a FONDECYT Regular grant (award no. 1221220). The authors would like to thank the referees for their valuable comments, which led to significant improvements of the original manuscript.

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Authors and Affiliations

  1. Department of Mathematics, University of Aegean, Karlovassi, Samos, Greece

    Ourania Drosinou & Christos V. Nikolopoulos

  2. Institute for Mathematical and Computational Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile

    Anastasios Matzavinos

  3. Department of Mathematics and Computer Science, Karlstad University, Karlstad, Sweden

    Nikos I. Kavallaris

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  1. Ourania Drosinou
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  2. Christos V. Nikolopoulos
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  3. Anastasios Matzavinos
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  4. Nikos I. Kavallaris
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Correspondence to Anastasios Matzavinos or Nikos I. Kavallaris.

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Drosinou, O., Nikolopoulos, C.V., Matzavinos, A. et al. A stochastic parabolic model of MEMS driven by fractional Brownian motion. J. Math. Biol. 86, 73 (2023). https://doi.org/10.1007/s00285-023-01897-6

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  • DOI: https://doi.org/10.1007/s00285-023-01897-6

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