Some singular equations modeling MEMS
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Publication:5122447
DOI10.1090/bull/1563zbMath1456.35193arXiv1706.02959OpenAlexW2562195364MaRDI QIDQ5122447
Christoph Walker, Philippe Laurençot
Publication date: 22 September 2020
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1706.02959
wave equationfree boundary problemwell-posednessbeam equationnonlocal nonlinearityfinite time singularitymicroelectromechanical system
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elasticity (74B20) Electromagnetic effects in solid mechanics (74F15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Free boundary problems for PDEs (35R35) Electro- and magnetostatics (78A30) PDEs in connection with mechanics of deformable solids (35Q74) Blow-up in context of PDEs (35B44) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial-boundary value problems for mixed-type systems of PDEs (35M33)
Related Items (24)
On the classification and evolution of bifurcation curves for a quasilinear regularized MEMS model ⋮ Shape derivative of the Dirichlet energy for a transmission problem ⋮ Stationary solutions to a nonlocal fourth-order elliptic obstacle problem ⋮ Wellposedness of a nonlinear parabolic-dispersive coupled system modelling MEMS ⋮ Taylor-Hood like finite elements for nearly incompressible strain gradient elasticity problems ⋮ Wellposedness of an elliptic-dispersive coupled system for MEMS ⋮ On semilinear elliptic equation with negative exponent arising from a closed MEMS model ⋮ The Effect of Diffusions and Sources on Semilinear Elliptic Problems ⋮ Heterogeneous Dielectric Properties in Models for Microelectromechanical Systems ⋮ New type super singular integro-differential equation and its conjugate equation ⋮ Qualitative analysis of a curvature equation modelling MEMS with vertical loads ⋮ Mathematical modelling and analysis of temperature effects in MEMS ⋮ Mellin transform and integro-differential equations with logarithmic singularity in the kernel ⋮ Touchdown is the only finite time singularity in a three-dimensional MEMS model ⋮ Reinforced limit of a MEMS model with heterogeneous dielectric properties ⋮ Convergence of energy minimizers of a MEMS model in the reinforced limit ⋮ On a free boundary model for three-dimensional MEMS with a hinged top plate: stationary case ⋮ A constrained model for MEMS with varying dielectric properties ⋮ Variational solutions to an evolution model for MEMS with heterogeneous dielectric properties ⋮ Singular behavior of an electrostatic-elastic membrane system with an external pressure ⋮ Regularity of extremal solutions of nonlocal elliptic systems ⋮ Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties ⋮ The Multidimensional Damped Wave Equation: Maximal Weak Solutions for Nonlinear Forcing via Semigroups and Approximation ⋮ Radial single point rupture solutions for a general MEMS model
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