相关论文: Global Dissipative Dynamics of the Extended Brusse…

The aim of this paper is to prove the existence and qualitative property of random attractors for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) on a semi-infinite interval with a Dirichlet boundary condition on the…

Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional…

The existence of a global attractor for wave equations in unbounded domains is a challenging problem due to the non-compactness of the Sobolev embeddings. To overcome this difficulty, some authors have worked with weighted Sobolev spaces…

In this paper we obtain the existence of global attractors for the dynamical systems generated by weak solution of the three-dimensional Navier-Stokes equations with damping. We consider two cases, depending on the values of the parameters…

The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is first proved that the trajectory field of the stochastic delayed…

We consider a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids with matched constant densities. This model consists of the Navier-Stokes system coupled with a convective nonlocal Cahn-Hilliard equation…

This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract…

We prove that the critical surface quasi-geostrophic equation driven by a force $f$ possesses a compact global attractor in $L^2(\mathbb T^2)$ provided $f\in L^p(\mathbb T^2)$ for some $p>2$. First, the De Giorgi method is used to obtain…

This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the $\beta$-plane. Previous results in this setting by M.A.H.…

We prove existence and uniqueness of global solutions for a class of reaction-advection-anisotropic-diffusion systems whose reaction terms have a "triangular structure". We thus extend previous results to the case of time-space dependent…

We study the asymptotic behavior of solutions of discrete nonlinear Schr\"odinger-type (DNLS) equations. For a conservative system, we consider the global in time solvability and the question of existence of standing wave solutions.…

We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a…

We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying…

We consider the characterization of global attractors $A_f$ for semiflows generated by scalar one-dimensional semilinear parabolic equations of the form $u_t = u_{xx} + f(u,u_x)$, defined on the circle $x\in S^1$, for a class of reversible…

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…

In this paper, we prove the existence of a compact global attractor for the flow generated by equation $$ \frac{\partial u}{\partial t}(x,t)+u(x,t)= \int_{\mathbb{R}^{N}}J(x-y)(f( u(y,t))dy+ h, \quad h > 0, \quad x\in \mathbb{R}^{N}, \quad…

In this paper we study the long-time behavior of a nonlocal Cahn-Hilliard system with singular potential, degenerate mobility, and a reaction term. In particular, we prove the existence of a global attractor with finite fractal dimension,…

In this paper we study a nonlocal reaction-diffusion equation in which the diffusion depends on the gradient of the solution. We prove first the existence and uniqueness of regular and strong solutions. Second, we obtain the existence of…

We establish the effective {\em finite dimensionality} of the dynamics corresponding to a flow-plate interaction PDE model arising in aeroelasticity: a nonlinear panel, in the absence of rotational inertia, immersed in an inviscid potential…

We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice $\mathbb{Z}$. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively.…