We study dynamical hysteresis in a simple class of nonlinear ordinary differential equations, namely first-order equations subject to sinusoidal forcing. The assumed nonlinearities are such that the area of the hysteresis loop vanishes as the forcing frequency tends to zero; in other words, there is no static hysteresis. Using regular and singular perturbation techniques, we derive the first te...

We present a finite element scheme for nonlinear fourth-order diffusion equations that arise for example in lubrication theory for the time evolution of thin films of viscous fluids. The equations are in general fourth-order degenerate parabolic, but in addition singular terms of second order may occur which model the effects of intermolecular forces or thermocapillarity. Discretizing the arisi...

whenever g > 0 is increasing and convex on R and superlinear at +∞ in the sense (7) stated below. Under these assumptions, the extremal parameter of (2) satisfies 0 < λ∗ < ∞. Here and throughout the paper, Ω is a smooth bounded domain of R . For each 0 ≤ λ < λ∗, the minimal solution of (2) is classical. Their limit as λ ↑ λ∗ is the extremal solution u∗ and it may be singular (i.e. unbounded) fo...

In this paper we present a new approach to design the input control to track the output of a non-minimum phase nonlinear system. Therefore, a ascade control scheme that combines input–output feedback linearization and gradient descent control method is proposed. Therein, input–output eedback linearization forms the inner loop that compensates the nonlinearities in the input–output behavior, and...

This paper presents a procedure for the identification of continuous-time systems with memoryless nonlinear feedback. The feedback nonlinear element, described by a bounded unknown function, is expressed as a linear combination of some base functions. Both the parameters of the feedforward linear system and of the nonlinear element representation are identified. To improve the representation of...

Kalman filters are widely used for data assimilation into ocean models. The aim of this study is to discuss the relevance of these filters with high resolution ocean models. This was investigated through the comparison of two advanced Kalman filters: the singular evolutive extended Kalman (SEEK) filter and its ensemble-based variant, called SEIK filter. The two filters were implemented with the...

The dynamics of micro/nanoelectromechanical systems (M/NEMS) is a core research area in micromechanics. Due to the nonlinearities and singular nature actuation forces that emerge these systems, it has become promising challenging area. foremost objective this manuscript examine M/NEMS by approximating rational terms involved structures. An switch under electromagnetic force adopted reveal effec...

We investigate entire radial solutions of the semilinear biharmonic equation ∆u = λ exp(u) in Rn, n ≥ 5, λ > 0 being a parameter. We show that singular radial solutions of the corresponding Dirichlet problem in the unit ball cannot be extended as solutions of the equation to the whole of Rn. In particular, they cannot be expanded as power series in the natural variable s = log |x|. Next, we pro...