Search results for "Nonlinear system"
showing 10 items of 1446 documents
Variable exponent p(x)-Kirchhoff type problem with convection
2022
Abstract We study a nonlinear p ( x ) -Kirchhoff type problem with Dirichlet boundary condition, in the case of a reaction term depending also on the gradient (convection). Using a topological approach based on the Galerkin method, we discuss the existence of two notions of solutions: strong generalized solution and weak solution. Strengthening the bound on the Kirchhoff type term (positivity condition), we establish existence of weak solution, this time using the theory of operators of monotone type.
Linearly implicit-explicit schemes for the equilibrium dispersive model of chromatography
2018
Abstract Numerical schemes for the nonlinear equilibrium dispersive (ED) model for chromatographic processes with adsorption isotherms of Langmuir type are proposed. This model consists of a system of nonlinear, convection-dominated partial differential equations. The nonlinear convection gives rise to sharp moving transitions between concentrations of different solute components. This property calls for numerical methods with shock capturing capabilities. Based on results by Donat, Guerrero and Mulet (Appl. Numer. Math. 123 (2018) 22–42), conservative shock capturing numerical schemes can be designed for this chromatography model. Since explicit schemes for diffusion problems can pose seve…
Constrained control of a nonlinear two point boundary value problem, I
1994
In this paper we consider an optimal control problem for a nonlinear second order ordinary differential equation with integral constraints. A necessary optimality condition in form of the Pontryagin minimum principle is derived. The proof is based on McShane-variations of the optimal control, a thorough study of their behaviour in dependence of some denning parameters, a generalized Green formula for second order ordinary differential equations with measurable coefficients and certain tools of convex analysis.
Nonsmooth Mechanics. Convex and Nonconvex Problems
1999
Nonlinear, multivalued and possibly nonmonotone relations arise in several areas of mechanics. A multivalued or complete relation is a relation with complete vertical branches. Boundary laws of this kind connect boundary (or interface) quantities. A contact relation or a locking mechanism between boundary displacements and boundary tractions in elasticity is a representative example. Material constitutive relations with complete branches connect stress and strain tensors, or, in simplified theories, equivalent stress and strain quantities. A locking material or a perfectly plastic one is represented by such a relation. The question of nonmonotonicity is more complicated. One aspect concerns…
Monotonicity and enclosure methods for the p-Laplace equation
2018
We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the $p$-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs, one of which is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.
Robust l2-gain control for 2D nonlinear stochastic systems with time-varying delays and actuator saturation
2013
Abstract This paper is concerned with the problems of stability analysis and l2-gain control for a class of two-dimensional (2D) nonlinear stochastic systems with time-varying delays and actuator saturation. Firstly, a convex hull representation is used to describe the saturation behavior, and a sufficient condition for the existence of mean-square exponential stability of the considered system is derived. Then, a state feedback controller which guarantees the resulting closed-loop system to be mean-square exponentially stable with l2-gain performance is proposed, and an optimization procedure to maximize the estimation of domain of attraction is also given. All the obtained results are for…
Enclosure method for the p-Laplace equation
2014
We study the enclosure method for the p-Calder\'on problem, which is a nonlinear generalization of the inverse conductivity problem due to Calder\'on that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, where the inclusion is modelled as a jump in the conductivity. The result is based on a monotonicity inequality and the properties of the Wolff solutions.
Unsupervised change detection with kernels
2012
In this paper an unsupervised approach to change detection relying on kernels is introduced. Kernel based clustering is used to partition a selected subset of pixels representing both changed and unchanged areas. Once the optimal clustering is obtained the estimated representatives (centroids) of each group are used to assign the class membership to all others pixels composing the multitemporal scenes. Different approaches of considering the multitemporal information are considered with accent on the computation of the difference image directly in the feature spaces. For this purpose a difference kernel approach is successfully adopted. Finally an effective way to cope with the estimation o…
Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model a…
2019
Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a compr…
Non-linear dynamics of alpha and theta rhythm: correlation dimensions and Lyapunov exponents from healthy subject's spontaneous EEG.
1997
The aim of the present paper was to analyze some non-linear dynamic properties of the resting EEG from healthy subjects under eyes closed conditions. For this purpose we digitally filtered the spontaneous EEG in the theta (3-8 Hz) and alpha frequency range (8-13 Hz) and considered these independent rhythms as signals from a deterministic system. Under certain conditions non-linear dynamic systems are able to generate deterministic chaos, which means that similar causes do not produce similar effects. This phenomenon is called sensitive dependence on initial conditions. From different lead positions (F3, F4, Cz, P3, P4, O1 and O2) we calculated the so-called correlation dimension D2, which i…