Back to Search
Start Over
Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties
Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties
- Source :
- Calculus of variations and partial differential equations 61 (2022), Nr. 1, Calculus of variations and partial differential equations, Calculus of Variations and Partial Differential Equations, Calculus of Variations and Partial Differential Equations, 2022, 61, pp.16
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This asymptotic model inherits the dielectric properties of the insulating layer. It involves the electrostatic potential in the device and the deformation of the elastic plate defining the geometry of the device. The electrostatic potential is given by an elliptic equation with mixed boundary conditions in the possibly non-Lipschitz region between the two plates. The deformation of the elastic plate is supposed to be a critical point of an energy functional which, in turn, depends on the electrostatic potential due to the force exerted by the latter on the elastic plate. The energy functional is shown to have a minimizer giving the geometry of the device. Moreover, the corresponding Euler–Lagrange equation is computed and the maximal regularity of the electrostatic potential is established.
- Subjects :
- Work (thermodynamics)
Regularized Model
Dielectric
01 natural sciences
35J50 - 49Q10 - 49J40 - 35R35 - 35Q74
Physics::Fluid Dynamics
Mathematics - Analysis of PDEs
obstacle problem
Critical point (thermodynamics)
Electrostatic Mems
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Boundary value problem
ddc:510
0101 mathematics
Minimizers
Mathematics
Energy functional
Microelectromechanical systems
Applied Mathematics
010102 general mathematics
Boundary-Value-Problems
Post-Touchdown Configurations
Mechanics
bilaplacian operator
Dewey Decimal Classification::500 | Naturwissenschaften::510 | Mathematik
010101 applied mathematics
Elliptic curve
shape derivative
Deformation (engineering)
Analysis
Analysis of PDEs (math.AP)
Subjects
Details
- ISSN :
- 09442669 and 14320835
- Database :
- OpenAIRE
- Journal :
- Calculus of variations and partial differential equations 61 (2022), Nr. 1, Calculus of variations and partial differential equations, Calculus of Variations and Partial Differential Equations, Calculus of Variations and Partial Differential Equations, 2022, 61, pp.16
- Accession number :
- edsair.doi.dedup.....3d6eda74db9c04a937d3f80ecf1e2d0e
- Full Text :
- https://doi.org/10.48550/arxiv.2003.14000