" Micro-and nanoelectromechanical systems (MEMS and NEMS), which combine electronics
with miniature-size mechanical devices, are essential components of modern technology. It …

This paper is devoted to the analysis of non-negative solutions for a generalisation of the
classical parabolic-elliptic Patlak–Keller–Segel system with d≥ 3 and porous medium-like …

The paper investigates a class of long-wave unstable lubrication model using Lie theory. A
nonlinear self-adjoint classification of the considered equation is carried out. Without having …

The behavior of a thin liquid film on a uniformly heated substrate is considered. When the
substrate is horizontal and the Marangoni number sufficiently large the film breaks up into a …

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations Page
1 Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations …

In this work, the initial-boundary value problem for the global dynamical properties of
solutions to a class of finite degenerate fourth-order parabolic equations with mean …

In this paper we investigate the large-time behavior of strong solutions to the one-
dimensional fourth order degenerate parabolic equation ut=−(uu xxx) x, modeling the …

In this paper, we study some quantitative properties of positive solutions to a singular elliptic
equation with negative power on the bounded smooth domain or in the whole Euclidean …

A new approach to the construction of entropies and entropy productions for a large class of
nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of …

We study the dynamics of dissipation and blow-up in a critical-case unstable thin film
equation. The governing equation is a nonlinear fourth-order degenerate parabolic PDE …