相关论文: Partial Inertial Manifolds for infinite-dimensiona…

This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify…

In this paper, we study the asymptotic behavior as $x_1\to+\infty$ of solutions of semilinear elliptic equations in quarter- or half-spaces, for which the value at $x_1=0$ is given. We prove the uniqueness and characterize the…

The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the application of exponential dichotomies to elliptic problems posed…

Spectral submanifolds (SSMs) are invariant manifolds of a dynamical system, defined by the property of being tangent to a spectral subspace of the linearized dynamics at a steady state. We show existence, along with certain desirable…

Noncommutative Euclidean spaces -- otherwise known as Moyal spaces or quantum Euclidean spaces -- are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the…

Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…

A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…

This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…

In this paper we study the representation of partial differential equations (PDEs) as abstract differential-algebraic equations (DAEs) with dissipative Hamiltonian structure (adHDAEs). We show that these systems not only arise when there…

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…

The notion of asymptotic unpredictability was recently introduced in (Commun. Nonlinear Sci. Numer. Simul. 134, 108029, 2024) for semiflows. Likewise unpredictable trajectories, asymptotically unpredictable ones are also capable of…

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential…

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…

In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…

A novel type of trajectory on semiflows, called asymptotically unpredictable, was proposed by Fen and Tokmak Fen [15]. The presence of sensitivity, which is an indispensable feature of chaotic dynamics, is a crucial property that arises…

In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum.

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…

We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the…

In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…