On a general family of nonautonomous elliptic and parabolic equations

DOI10.1007/s00526-009-0262-1zbMath1186.35215OpenAlexW2038413314MaRDI QIDQ848875

Dong Ye, Feng Zhou

Publication date: 23 February 2010

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-009-0262-1

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) PDEs in connection with optics and electromagnetic theory (35Q60) Semilinear elliptic equations (35J61) Blow-up in context of PDEs (35B44)

Related Items (16)

Self-similar solutions for a quenching problem with spatially dependent nonlinearity ⋮ On some touchdown behaviors of the generalized MEMS device equation ⋮ Positivity-preserving and unconditionally energy stable numerical schemes for MEMS model ⋮ Asymptotic and quenching behaviors of semilinear parabolic systems with singular nonlinearities ⋮ Critical pull-in curves of MEMS actuators in presence of Casimir force ⋮ On semi‐linear elliptic equation arising from Micro‐Electromechanical Systems with contacting elastic membrane ⋮ Quenching phenomenon for a parabolic MEMS equation ⋮ On a parabolic equation in MEMS with fringing field ⋮ On semilinear elliptic equation with negative exponent arising from a closed MEMS model ⋮ Regularity of the extremal solution for some elliptic problems with singular nonlinearity and advection ⋮ Viscosity dominated limit of global solutions to a hyperbolic equation in MEMS ⋮ Dynamical solutions of singular parabolic equations modeling electrostatic MEMS ⋮ Estimates for the quenching time of a MEMS equation with fringing field ⋮ On the quenching behavior of the MEMS with fringing field ⋮ Singular behavior of an electrostatic-elastic membrane system with an external pressure ⋮ Dynamics of electrostatic microelectromechanical systems actuators

Cites Work

• Unnamed Item
• Unnamed Item
• 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
• Estimates for the quenching time of a parabolic equation modeling electrostatic MEMS
• Quenching, nonquenching, and beyond quenching for solution of some parabolic equations
• On the quenching behavior of the solution of a semilinear parabolic equation
• Mathematical Modeling of Electrostatic MEMS with Tailored Dielectric Properties
• BOUNDEDNESS OF THE EXTREMAL SOLUTION FOR SEMILINEAR ELLIPTIC PROBLEMS
• Analysis of the Dynamics and Touchdown in a Model of Electrostatic MEMS
• On the Partial Differential Equations of Electrostatic MEMS Devices: Stationary Case
• A Criterion for Blow-Up of Solutions to Semilinear Heat Equations
• Sur une classe de problemes non lineaires avec non linearite positive, croissante, convexe.
• Regularity of the extremal solution of semilinear elliptic equations
• A nonlocal quenching problem arising in a micro-electro mechanical system
• Nonlinear non-local elliptic equation modelling electrostatic actuation
• Touchdown and Pull-In Voltage Behavior of a MEMS Device with Varying Dielectric Properties
• Remarks on quenching
• Nonlocal problems in MEMS device control

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