Seminar 28.11.2019: Annalisa Iuorio

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 28.11.2019: Annalisa Iuorio

Postby quittner » Mon Nov 18, 2019 10:51 am

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Thursday 28.11.2019 at 14:00 Lecture room M-223

Annalisa Iuorio (RICAM Linz)
Singular Perturbation Analysis of a Regularized MEMS Model

Abstract:
Micro-Electro Mechanical Systems (MEMS) are defined as very small structures
that combine electrical and mechanical components on a common substrate.
Here, the electrostatic-elastic case is considered, where an elastic membrane
is allowed to deflect above a ground plate under the action of an electric
potential, whose strength is proportional to a parameter.
Such devices are commonly described by a parabolic partial differential
equation that contains a singular nonlinear source term.
The singularity in that term corresponds to the so-called "touchdown"
phenomenon, where the membrane establishes contact with the ground plate.
Touchdown is known to imply the non-existence of steady state solutions
and blow-up of solutions in finite time. In this talk we analyze
a recently proposed extension of that canonical model, where such
singularities are avoided due to the introduction of a regularizing term
involving a small "regularization" parameter.
Methods from dynamical systems and geometric singular perturbation theory,
in particular the desingularization technique known as "blow-up", allow
for a precise description of steady-state solutions of the regularized model,
as well as for a detailed resolution of the resulting bifurcation diagram.
The interplay between the two main model parameters is emphasized;
in particular, the focus is on the singular limit as both parameters
tend to zero. This is a joint work with Nikola Popovic and Peter Szmolyan.
quittner
 
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