### Abstract

The formation of finite time singularities in a nonlinear parabolic fourth order partial differential equation (PDE) is investigated for a variety of two-dimensional geometries. The PDE is a variant of a canonical model for Micro-Electro Mechanical systems (MEMS). The singularities are observed to form at specific points in the domain and correspond to solutions whose values remain finite but whose derivatives diverge as the finite time singularity is approached. This phenomenon is known as quenching. An asymptotic analysis reveals that the quenching set can be predicted by simple geometric considerations suggesting that the phenomenon described is generic to higher order parabolic equations which exhibit finite time singularity.

Original language | English (US) |
---|---|

Pages (from-to) | 807-834 |

Number of pages | 28 |

Journal | Journal of Nonlinear Science |

Volume | 23 |

Issue number | 5 |

DOIs | |

State | Published - Oct 2013 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bi-Laplace equations
- Finite time singularity
- MEMS
- Nanotechnology
- Singular perturbation theory

### ASJC Scopus subject areas

- Applied Mathematics
- Modeling and Simulation
- Engineering(all)

### Cite this

*Journal of Nonlinear Science*,

*23*(5), 807-834. https://doi.org/10.1007/s00332-013-9169-2

**The quenching set of a MEMS capacitor in two-dimensional geometries.** / Lindsay, A. E.; Lega, Joceline C; Sayas, F. J.

Research output: Contribution to journal › Article

*Journal of Nonlinear Science*, vol. 23, no. 5, pp. 807-834. https://doi.org/10.1007/s00332-013-9169-2

}

TY - JOUR

T1 - The quenching set of a MEMS capacitor in two-dimensional geometries

AU - Lindsay, A. E.

AU - Lega, Joceline C

AU - Sayas, F. J.

PY - 2013/10

Y1 - 2013/10

N2 - The formation of finite time singularities in a nonlinear parabolic fourth order partial differential equation (PDE) is investigated for a variety of two-dimensional geometries. The PDE is a variant of a canonical model for Micro-Electro Mechanical systems (MEMS). The singularities are observed to form at specific points in the domain and correspond to solutions whose values remain finite but whose derivatives diverge as the finite time singularity is approached. This phenomenon is known as quenching. An asymptotic analysis reveals that the quenching set can be predicted by simple geometric considerations suggesting that the phenomenon described is generic to higher order parabolic equations which exhibit finite time singularity.

AB - The formation of finite time singularities in a nonlinear parabolic fourth order partial differential equation (PDE) is investigated for a variety of two-dimensional geometries. The PDE is a variant of a canonical model for Micro-Electro Mechanical systems (MEMS). The singularities are observed to form at specific points in the domain and correspond to solutions whose values remain finite but whose derivatives diverge as the finite time singularity is approached. This phenomenon is known as quenching. An asymptotic analysis reveals that the quenching set can be predicted by simple geometric considerations suggesting that the phenomenon described is generic to higher order parabolic equations which exhibit finite time singularity.

KW - Bi-Laplace equations

KW - Finite time singularity

KW - MEMS

KW - Nanotechnology

KW - Singular perturbation theory

UR - http://www.scopus.com/inward/record.url?scp=84884670919&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884670919&partnerID=8YFLogxK

U2 - 10.1007/s00332-013-9169-2

DO - 10.1007/s00332-013-9169-2

M3 - Article

AN - SCOPUS:84884670919

VL - 23

SP - 807

EP - 834

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

IS - 5

ER -