The course aims at presenting an introduction to the subject of singularity formation in
nonlinear evolution problems usually known as blowup. In short, we are interested in the …

The pull-in voltage instability associated with a simple MEMS device, consisting of a thin
dielectric elastic membrane supported above a rigid conducting ground plate, is analyzed …

Degenerate neckpinches in mean curvature flow Page 1 j. reine angew. Math. 482 (1997),
15—66 Journal fr die reine und angewandte Mathematik © Walter de Gruyter Berlin · New …

Quenching phenomena play important roles in both steady and unsteady combustion
processes. This article studies a compound finite difference method for solving a nonlinear …

The aims of this paper are to investigate and propose a numerical approximation for a
quenching type diffusion problem associated with a two-sided Riemann-Liouville space …

In this paper, we study an evolution problem arises in the study of MEMS (micro-electro
mechanical system) device. We consider both parabolic and hyperbolic type problems. We …

In this paper, we study a nonlocal parabolic problem arising in the study of a micro-electro
mechanical system. The nonlocal nonlinearity involved is related to an integral over the …

In this paper, we are interested in the mathematical model of MEMS devices which is
presented by the following equation on (0, T)× Ω:∂ tu= Δ u+ λ (1− u) 2 (1+ γ∫ Ω 1 1− udx) 2 …

Rupture is a nonlinear instability resulting in a finite-time singularity as a film layer
approaches zero thickness at a point. We study the dynamics of rupture in a generalized …

We prove global existence of nonnegative solutions to the singular parabolic equation $ u_t-
\Delta u+\chi _ {\{u> 0\}}(-u^{-\beta}+\lambda f (u))= 0$ in a smooth bounded domain …