相关论文: Global attractors for a full von Karman beam trans…

For a class of quasilinear parabolic systems with nonlinear Robin boundary conditions we construct a compact local solution semiflow in a nonlinear phase space of high regularity. We further show that a priori estimates in lower norms are…

In the article, we aim to investigate the well-posedness of solution and the regularity of the global attractor for the couple stress fluid in saturated porous media with the local thermal non-equilibrium effect. To be more specific, we…

We prove the existence of a compact, finite dimensional, global attractor for a coupled PDE system comprising a nonlinearly damped semilinear wave equation and a nonlinear system of thermoelastic plate equations, without any mechanical…

This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in…

This paper considers the dynamical behavior of solutions of constitutive systems for 1D compressible viscous and heat-conducting micropolar fluids. With proper constraints on initial data, we prove the existence of global attractors in…

In this paper we prove the existence of the global attractor for the wave equation with nonlocal weak damping, nonlocal anti-damping and critical nonlinearity.

In this work the existence of a global attractor for the solution semiflow of the coupled two-cell Brusselator model equations is proved. A grouping estimation method and a new decomposition approach are introduced to deal with the…

While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…

We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and the classical (nonlinear) elastic plate equation for in-plane motions on a flexible flat part of the boundary. The…

The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous…

We consider the wave equation with degenerate viscoelastic dissipation recently examined in Cavalcanti, Fatori, and Ma, Attractors for wave equations with degenerate memory, J. Differential Equations (2016). Under some additional…

We consider a nonlinear (Berger or Von Karman) clamped plate model with a {\em piston-theoretic} right hand side---which include non-dissipative, non-conservative lower order terms. The model arises in aeroelasticity when a panel is…

We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS-BEC crossover. First, we prove that the initial boundary value problem generates a strongly continuous semigroup on a…

We study a two-phase modified Stefan problem modeling solid combustion and nonequilibrium phase transition. The problem is known to exhibit a variety of non-trivial dynamical scenarios. We develop a priori estimates and establish…

We consider a 2D system that models the nematic liquid crystal flow through the Navier--Stokes equations suitably coupled with a transport-reaction-diffusion equation for the averaged molecular orientations. This system has been proposed as…

We consider a family of non-autonomous reaction-diffusion equations with almost periodic, rapidly oscillating principal part and nonlinear interactions. As the frequency of the oscillations tends to infinity, we prove that the solutions of…

We study well-posedness and asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) full von Karman shallow shell equations that accounts for both…

We consider dynamical behavior of non-autonomous wave-type evolutionary equations with nonlinear damping, critical nonlinearity, and time-dependent external forcing which is translation bounded but not translation compact (i.e., external…

The analysis of the long-term behavior of the mathematical model of a neural network constitutes a suitable framework to develop new tools for the dynamical description of nonautonomous state-dependent delay equations (SDDEs). The concept…

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…