On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control

DOI10.1016/j.na.2016.02.001zbMath1334.35340arXiv1602.07888OpenAlexW2287584166MaRDI QIDQ272747

Nikos I. Kavallaris, Christos V. Nikolopoulos, Andrew A. Lacey

Publication date: 20 April 2016

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.07888

zbMATH Keywords

quenchingelectrostatic MEMStouchdown

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics (74H35) Nonlinear elliptic equations (35J60) Membranes (74K15) PDEs in connection with mechanics of deformable solids (35Q74) Qualitative behavior of solutions of equilibrium problems in solid mechanics (74G55)

Related Items

Quenching study of two-dimensional fractional reaction-diffusion equation from combustion process, Some singular equations modeling MEMS, A stochastic parabolic model of MEMS driven by fractional Brownian motion, Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer–Meinhardt system, A note on the adaptive numerical solution of a Riemann-Liouville space-fractional Kawarada problem, Bifurcation diagram of a Robin boundary value problem arising in MEMS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a nonlocal parabolic problem arising in electrostatic MEMS control
• A hyperbolic non-local problem modelling MEMS technology
• The existence and dynamic properties of a parabolic nonlocal MEMS equation
• On the partial differential equations of electrostatic MEMS devices. III: Refined touchdown behavior
• On the partial differential equations of electrostatic MEMS devices. II: Dynamic case
• How to adaptively resolve evolutionary singularities in differential equations with symmetry
• Some dichotomy results for the quenching problem
• A nonlinear heat equation with singular initial data
• Semilinear parabolic equations with prescribed energy
• Touchdown and related problems in electrostatic MEMS device equation
• Quasilinear Dirichlet problems driven by positive sources
• Analysis of the Dynamics and Touchdown in a Model of Electrostatic MEMS
• Quenching profiles for one-dimensional semilinear heat equations
• A nonlocal quenching problem arising in a micro-electro mechanical system
• Touchdown and Pull-In Voltage Behavior of a MEMS Device with Varying Dielectric Properties
• On the growth of solutions of quasi‐linear parabolic equations
• ON THE BLOW-UP OF THE NON-LOCAL THERMISTOR PROBLEM
• Nonlocal problems in MEMS device control