相关论文: Exponential attractors with explicit fractal dimen…
In this paper we propose a new model of random graph directed fractals that extends the current well-known model of random graph directed iterated function systems, $V$-variable attractors, and fractal and Mandelbrot percolation. We study…
In this paper, we approach the problem of finding the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space via an implicit forward-backward-forward dynamical system with…
This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of…
We describe a class of fractal attractors induced by \beta-shifts. We use a coding by these shifts to show that the systems are mixing with topological entropy log \beta and have an ergodic measure of full entropy. Moreover we determine the…
This article is devoted to the study of the existence of an exponential attractor for a family of problems, in which diffusion $d_{\lambda}$ blows up in localized regions inside the domain, \begin{equation*} \begin{cases} \displaystyle…
In this work, we explore the dynamics of fractional differential equations (FDEs) through a rigorous topological analysis of strange attractors. By investigating systems with Caputo derivatives of order \( \alpha \in (0, 1) \), we identify…
In this article we study the long-time behaviour of a system of nonlinear Partial Differential Equations (PDEs) modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic field. We…
A new antidynamo theorem for non-stretched twisted magnetic flux tube dynamo is obtained. Though Riemannian curvature cannot be neglected since one considers curved magnetic flux tube axis, the stretch can be neglect since one only…
In this paper we investigate four concepts of exponential stability for difference equations in Banach spaces. Characterizations of these concepts are given. They can be considered as variants for the discrete-time case of the classical…
We consider a two-dimensional nonstationary Navier-Stokes shear flow with a subdifferential boundary condition on a part of the boundary of the flow domain, namely, with a boundary driving subject to the Tresca law. There exists a unique…
This paper proposes an abstract theory concerned with dynamical systems generated by doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations in a reflexive Banach space setting. In order to…
In this paper, the existence, uniqueness, and positivity of solutions, as well as the asymptotic behavior through a finite fractal dimensional global attractor for a general Advection-Diffusion-Reaction (ADR) equation, are investigated. Our…
In the paper, we define a class of new fractals named ``non-autonomous attractors", which are the generalization of classic Moran sets and attractors of iterated function systems. Simply to say, we replace the similarity mappings by…
In this article we revisit the perturbation of exponential trichotomy of linear difference equation in Banach space by using a Perron-Lyapunov fixed point formulation for the perturbed evolution operator. This approach allows us to directly…
Localized states of Harper's equation correspond to strange nonchaotic attractors (SNAs) in the related Harper mapping. In parameter space, these fractal attractors with nonpositive Lyapunov exponents occur in fractally organized…
This paper is concerned with the asymptotic behavior of solutions of the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. We first introduce a continuous…
We construct a Hereditarily Indecomposable Banach space $\eqs_d$ with a Schauder basis \seq{e}{n} on which there exist strictly singular non-compact diagonal operators. Moreover, the space $\mc{L}_{\diag}(\eqs_d)$ of diagonal operators with…
The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of normed spaces can be described as a union of disjoint…
This article discusses the weak pullback attractors for a damped stochastic fractional Schr\"odinger equation on $\mathbb{R}^n$ with $n\geq 2$. By utilizing the stochastic Strichartz estimates and a stopping time technique argument, the…
The paper gives a detailed study of long-time dynamics generated by weakly damped wave equations in bounded 3D domains where the damping exponent depends explicitly on time and may change sign. It is shown that in the case when the…