Finite time singularity in a free boundary problem modeling MEMS

DOI10.1016/j.crma.2013.10.004zbMath1290.35259arXiv1305.7407OpenAlexW2149587902MaRDI QIDQ387780

Joachim Escher, Philippe Laurençot, Christoph Walker

Publication date: 17 December 2013

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.7407

zbMATH Keywords

free boundary problemsfinite time singularity

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (13)

On qualitative properties of solutions to microelectromechanical systems with general permittivity ⋮ The Time Singular Limit for a Fourth-Order Damped Wave Equation for MEMS ⋮ Finite-time singularities of solutions to microelectromechanical systems with general permittivity ⋮ A free boundary value problem modelling microelectromechanical systems with general permittivity ⋮ Some singular equations modeling MEMS ⋮ Touchdown is the only finite time singularity in a three-dimensional MEMS model ⋮ 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 variational approach to a stationary free boundary problem modeling MEMS ⋮ A qualitative analysis of solutions to microelectromechanical systems with curvature and nonlinear permittivity profile ⋮ Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium analysis ⋮ Dynamics of a free boundary problem with curvature modeling electrostatic MEMS ⋮ The abstract quasilinear Cauchy problem for a MEMS model with two free boundaries

Cites Work

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• Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity
• A stationary free boundary problem modeling electrostatic MEMS
• A parabolic free boundary problem modeling electrostatic MEMS
• A free boundary problem in the theory of electrically actuated microdevices
• Non-linear effects on canonical MEMS models
• Analysis of the Dynamics and Touchdown in a Model of Electrostatic MEMS
• Dynamics of a free boundary problem with curvature modeling electrostatic MEMS
• Touchdown and Pull-In Voltage Behavior of a MEMS Device with Varying Dielectric Properties

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