Asymptotics of some nonlinear eigenvalue problems for a MEMS capacitor: Part I: Fold point asymptotics

DOI10.4310/MAA.2008.v15.n3.a4zbMath1173.35625MaRDI QIDQ1021004

Alan E. Lindsay, Michael J. Ward

Publication date: 4 June 2009

Published in: Methods and Applications of Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.maa/1239396532

zbMATH Keywords

matched asymptotic expansionsnonlinear eigenvalue problemboundary layerpseudo-arclength continuationshootingfold point

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Singular perturbations in context of PDEs (35B25) Asymptotic expansions of solutions to PDEs (35C20) Membranes (74K15) Bifurcations in context of PDEs (35B32)

Related Items (19)

Convergence of solutions of a nonlocal biharmonic MEMS equation with the fringing field ⋮ Vanishing aspect ratio limit for a fourth-order MEMS model ⋮ The quenching set of a MEMS capacitor in two-dimensional geometries ⋮ The structure of stationary solutions to a micro-electro mechanical system with fringing field ⋮ On a parabolic equation in MEMS with fringing field ⋮ A note on model reduction for microelectromechanical systems ⋮ Some singular equations modeling MEMS ⋮ Variational approach to MEMS model with fringing field ⋮ Asymptotic Analysis of Localized Solutions to Some Linear and Nonlinear Biharmonic Eigenvalue Problems ⋮ Dynamical solutions of singular parabolic equations modeling electrostatic MEMS ⋮ On MEMS equation with fringing field ⋮ Regularized model of post-touchdown configurations in electrostatic MEMS: bistability analysis ⋮ Estimates for the quenching time of a MEMS equation with fringing field ⋮ On the existence of positive solutions for some nonlinear boundary value problems and applications to MEMS models ⋮ A numerical study of the pull-in instability in some free boundary models for MEMS ⋮ A semilinear problem with a gradient term in the nonlinearity ⋮ Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium analysis ⋮ Fringing field can prevent infinite time quenching ⋮ Radial regular and rupture solutions for a PDE problem with gradient term and two parameters

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