Asymptotics of some nonlinear eigenvalue problems modelling a MEMS Capacitor. Part II: multiple solutions and singular asymptotics

DOI10.1017/S0956792510000318zbMath1220.35108MaRDI QIDQ3168754

Michael J. Ward, Alan E. Lindsay

Publication date: 19 April 2011

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

matched asymptoticsnonlinear eigenvaluesswitchback terms

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Singular perturbations in context of PDEs (35B25) Membranes (74K15) Singular elliptic equations (35J75)

Related Items (14)

A fourth-order model for MEMS with clamped boundary conditions ⋮ Vanishing aspect ratio limit for a fourth-order MEMS model ⋮ The quenching set of a MEMS capacitor in two-dimensional geometries ⋮ Hotspot formation and dynamics for a continuum model of urban crime ⋮ Some singular equations modeling MEMS ⋮ Singular Perturbation Analysis of a Regularized MEMS Model ⋮ Regularized model of post-touchdown configurations in electrostatic MEMS: bistability analysis ⋮ Refinements to the study of electrostatic deflections: theory and experiment ⋮ Point Ruptures for a MEMS Equation with Fringing Field ⋮ Non-linear effects on canonical MEMS models ⋮ Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium analysis ⋮ The Transition to a Point Constraint in a Mixed Biharmonic Eigenvalue Problem ⋮ The onset of multi-valued solutions of a prescribed mean curvature equation with singular non-linearity ⋮ Radial single point rupture solutions for a general MEMS model

Cites Work

• Asymptotic behavior of touch-down solutions and global bifurcations for an elliptic problem with a singular nonlinearity
• A geometric analysis of the Lagerstrom model problem
• Rigorous asymptotic expansions for Lagerstrom's model equation -- a geometric approach
• Asymptotic behaviour of the Kazdan-Warner solution in the annulus
• The effect of the small-aspect-ratio approximation on canonical electrostatic MEMS models
• Mathematical Modeling of Electrostatic MEMS with Tailored Dielectric Properties
• Estimates on Pull-In Distances in Microelectromechanical Systems Models and Other Nonlinear Eigenvalue Problems
• Note on Logarithmic Switchback Terms in Regular and Singular Perturbation Expansions
• On a Fourth Order Nonlinear Elliptic Equation with Negative Exponent
• Infinitely many turning points for an elliptic problem with a singular non-linearity
• On the Partial Differential Equations of Electrostatic MEMS Devices: Stationary Case
• Compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity
• Nonlinear non-local elliptic equation modelling electrostatic actuation
• Symmetry of non-negative solutions of a semilinear elliptic equation with singular nonlinearity
• Touchdown and Pull-In Voltage Behavior of a MEMS Device with Varying Dielectric Properties

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