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We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This development extends an existing framework for well-posed problems and…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
Flexible grid topology has become a key enabler of flexibility in modern power grids, particularly for congestion management. Studying the effects of combinatorial topological changes is therefore of significant interest, though it remains…
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
The aim of this work is to consider the internal stabilization of a nonlinear coupled system of two Korteweg--de Vries equations in a finite interval under the effect of a very weak localized damping. The system was introduced by Gear and…
In this note we provide some precise estimates explaining the diffusive structure of partially dissipative systems with time-dependent coefficients satisfying a uniform Kalman rank condition. Precisely, we show that under certain (natural)…
Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the…
We propose a framework for studying the stability of discrete-event systems modelled as switching max-plus linear systems. In this framework, we propose a set of notions of stability for generic discrete-event systems in the max-plus…
This paper investigates the stability and stabilization of semilinear single-track vehicle models with distributed tire friction dynamics, modeled as interconnections of ordinary differential equations (ODEs) and hyperbolic partial…
Localized spot patterns, where one or more solution components concentrates at certain points in the domain, are a common class of localized pattern for reaction-diffusion systems, and they arise in a wide range of modeling scenarios. In an…
We develop an inertial coupling method for modeling the dynamics of point-like 'blob' particles immersed in an incompressible fluid, generalizing previous work for compressible fluids. The coupling consistently includes excess (positive or…
This paper addresses the problem of exponential and accelerated finite-time, as well as nearly fixed-time, stabilization of switched linear MIMO systems. The proposed approach relies on a generalized homogenization framework for switched…
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The results are obtained by constructing and studying the…
We consider two classical macrospins with dynamical (frequency-dependent) coupling, modeled by a generalized Landau-Lifshitz-Gilbert equation. We show that, in the absence of local damping, the resulting dynamics are pseudo-Hermitian. When…
This paper is concerned with the calmness of a partial perturbation to the composite rank constraint system, an intersection of the rank constraint set and a general closed set, which is shown to be equivalent to a local Lipschitz-type…