1,720,973 research outputs found
Global Solvability of Dirichlet Problem for Fully Nonlinear Elliptic Systems
No full textWe show existence theorems of global strong solutions of Dirichlet problem for second order fully
nonlinear systems that satisfy the Campanato’s condition of ellipticity. We use the Campanato’s near
operators theory
Recent applications of near operators Campanato's theory to study complex problems
No full textThis paper contains a short survey of the last applications of Campanato’s near operators theory. In partic-
ular we give an example of its applications to the proof of existence of a solution of the Cauchy-Dirichlet
problem concerning a class of fully nonlinear parabolic systems
Von Karman Equations
No full textWe show a new theorem in Campanato’s near operators theory and give an example of one of its applications to a
classical problem in the nonlinear elasticity theory: Von Kármán equations
A 2D non-linear second-order differential model for electrostatic circular membrane MEMS devices: A result of existence and uniqueness
No full textIn the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of the existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured
Nonlocal dynamic problems with singular nonlinearities and applications to MEMS
No full textWe establish existence and regularity results for a time dependent fourth-order integro-differential equation with a possibly singular nonlinearity which has applications in designing MicroElectroMechanicalSystems. The key ingredient in our approach, besides basic theory of hyperbolic equations in Hilbert spaces, exploits the Near Operators Theory introduced by Campanato
A 2D membrane MEMS device model with fringing field: Curvature-dependent electrostatic field and optimal control
No full textAn important problem in membrane micro-electric-mechanical-system (MEMS) modeling is the fringing-field phenomenon, of which the main effect consists of force-line deformation of electrostatic field E near the edges of the plates, producing the anomalous deformation of the membrane when external voltage V is applied. In the framework of a 2D circular membrane MEMS, representing the fringing-field effect depending on |u|2 with the u profile of the membrane, and since strong E produces strong deformation of the membrane, we consider |E| proportional to the mean curvature of the membrane, obtaining a new nonlinear second-order differential model without explicit singularities. In this paper, the main purpose was the analytical study of this model, obtaining an algebraic condition ensuring the existence of at least one solution for it that depends on both the electromechanical properties of the material constituting the membrane and the positive parameter δ that weighs the terms |u|2. However, even if the the study of the model did not ensure the uniqueness of the solution, it made it possible to achieve the goal of finding a stable equilibrium position. Moreover, a range of admissible values of V were obtained in order, on the one hand, to win the mechanical inertia of the membrane and, on the other hand, to ensure that the membrane did not touch the upper disk of the device. Lastly, some optimal control conditions based on the variation of potential energy are presented and discussed
Solution Properties of a New Dynamic Model for MEMS with Parallel Plates in the Presence of Fringing Field
No full textIn this paper, starting from a well-known nonlinear hyperbolic integro-differential model of the fourth order describing the dynamic behavior of an electrostatic MEMS with a parallel plate, the authors propose an upgrade of it by formulating an additive term due to the effects produced by the fringing field and satisfying the Pelesko–Driscoll theory, which, as is well known, has strong experimental confirmation. Exploiting the theory of hyperbolic equations in Hilbert spaces, and also utilizing Campanato’s Near Operator Theory (and subsequent applications), results of existence and regularity of the solution are proved and discussed particularly usefully in anticipation of the development of numerical approaches for recovering the profile of the deformable plate for a wide range of applications
Curvature Dependent Electrostatic Field in the Deformable MEMS Device: Stability and Optimal Control
No full textThe recovery of the membrane profile of an electrostatic micro-electro-mechanical system (MEMS) device is an important issue because, when applying an external voltage, the membrane deforms with the consequent risk of touching the upper plate of the device (a condition that should be avoided). Then, during the deformation of the membrane, it is useful to know if this movement admits stable equilibrium configurations. In such a context, our present work analyze the behavior of an electrostatic 1D membrane MEMS device when an external electric voltage is applied. In particular, starting from a well-known second-order elliptical semi-linear di erential model, obtained considering the electrostatic field inside the device proportional to the curvature of the membrane, the only possible equilibrium position is obtained, and its stability is analyzed. Moreover, considering that the membrane has an inertia in moving and taking into account that it must not touch the upper plate of the device, the range of possible values of the applied external voltage is obtained, which accounted for these two particular operating conditions. Finally, some calculations about the variation of potential energy have identified optimal control conditions
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