Dynamics of a free boundary problem with curvature modeling electrostatic MEMS

DOI10.1090/S0002-9947-2014-06320-4zbMath1325.35291arXiv1302.6026MaRDI QIDQ5251611

Joachim Escher, Christoph Walker, Philippe Laurençot

Publication date: 20 May 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.6026

zbMATH Keywords

free boundary problemasymptotic stabilitywell-posednesscurvatureMEMSsmall aspect ratio limit

Mathematics Subject Classification ID

Control, switches and devices (``smart materials) in solid mechanics (74M05) Singular perturbations in context of PDEs (35B25) Free boundary problems for PDEs (35R35) PDEs in connection with mechanics of deformable solids (35Q74) Initial-boundary value problems for mixed-type systems of PDEs (35M33)

Related Items (15)

The Time Singular Limit for a Fourth-Order Damped Wave Equation for MEMS ⋮ Finite-time singularities of solutions to microelectromechanical systems with general permittivity ⋮ Finite time singularity in a free boundary problem modeling MEMS ⋮ A free boundary value problem modelling microelectromechanical systems with general permittivity ⋮ Some singular equations modeling MEMS ⋮ Mathematical modelling and analysis of temperature effects in MEMS ⋮ A free boundary problem modeling electrostatic MEMS: I. Linear bending effects ⋮ Well-posedness of a quasilinear evolution problem modelling MEMS with general permittivity ⋮ A survey on second order free boundary value problems modelling MEMS with general permittivity profile ⋮ A new model for electrostatic MEMS with two free boundaries ⋮ On the existence of positive solutions for some nonlinear boundary value problems and applications to MEMS models ⋮ A variational approach to a stationary free boundary problem modeling MEMS ⋮ A qualitative analysis of solutions to microelectromechanical systems with curvature and nonlinear permittivity profile ⋮ On the principle of linearized stability in interpolation spaces for quasilinear evolution equations ⋮ The abstract quasilinear Cauchy problem for a MEMS model with two free boundaries

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