27 research outputs found
On the quenching behaviour of a semilinear wave equation modelling MEMS technology
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series A following peer review. The definitive publisher-authenticated version 2015, 35(3), pp. 1009-1037 is available online at: http://dx.doi.org/10.3934/dcds.2015.35.100
Hyperbolic quenching problem with damping in the micro-electro mechanical system device
[[abstract]]We study the initial boundary value problem for the damped hyperbolic
equation arising in the micro-electro mechanical system device with
local or nonlocal singular nonlinearity. For both cases, we provide some criteria
for quenching and global existence of the solution. We also derive the
existence of the quenching curve for the corresponding Cauchy problem with
local source[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[countrycodes]]US
The Role of Critical Exponents in Blowup Theorems
In this article various extensions of an old result of Fujita are considered for the initial value problem for the reaction-diffusion equation in with and nonnegative initial values. Fujita showed that if , then the initial value problem had no nontrivial global solutions while if , there were nontrivial global solutions. This paper discusses similar results for other geometries and other equations including a nonlinear wave equation and a nonlinear Schrödinger equation
A study of a nonlocal problem with Robin boundary conditions arising from technology
From Wiley via Jisc Publications RouterHistory: received 2020-08-03, rev-recd 2021-02-18, accepted 2021-02-22, pub-electronic 2021-05-04Article version: VoRPublication status: PublishedIn the current work, we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (micro‐electro‐mechanical system) device, when the ends of the device are attached or pinned to a cantilever. Initially, the steady‐state problem is investigated estimates of the pull‐in voltage are derived. In particular, a Pohožaev's type identity is also obtained, which then facilitates the derivation of an estimate of the pull‐in voltage for radially symmetric N‐dimensional domains. Next a detailed study of the time‐dependent problem is delivered and global‐in‐time as well as quenching results are obtained for generic and radially symmetric domains. The current work closes with a numerical investigation of the presented nonlocal model via an adaptive numerical method. Various numerical experiments are presented, verifying the previously derived analytical results as well as providing new insights on the qualitative behavior of the studied nonlocal model
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