相关论文: Asymptotic Behavior of neural fields in an unbound…

In this paper we consider the non local evolution equation $$ \frac{\partial u(x,t)}{\partial t} + u(x,t)= \int_{\mathbb{R}^{N}}J(x-y)f(u(y,t))\rho(y)dy+ h(x). %\,\,\, h \geq 0. $$ We show that this equation defines a continuous flow in…

In this work we consider the nonlocal evolution equation $$ \frac{\partial u(w,t)}{\partial t}=-u(w,t)+ \int_{S^{1}}J(wz^{-1})f(u(z,t))dz+ h, \,\,\, h > 0 $$ which arises in models of neuronal activity, in $L^{2}(S^{1})$, where $S^{1}$…

We prove the existence of a global attractor for the Newton-Boussinesq equation defined in a two-dimensional channel. The asymptotic compactness of the equation is derived by the uniform estimates on the tails of solutions. We also…

In this work we consider the non local evolution problem \[ \begin{cases} \partial_t u(x,t)=-u(x,t)+g(\beta K(f\circ u)(x,t)+\beta h), ~x \in\Omega, ~t\in[0,\infty[;\\ u(x,t)=0, ~x\in\mathbb{R}^N\setminus\Omega, ~t\in[0,\infty[;\\…

We prove that the weakly damped cubic Schr\"odinger flow in $L^2(\T)$ provides a dynamical system that possesses a global attractor. The proof relies on a sharp study of the behavior of the associated flow-map with respect to the weak $…

Under fairly general assumptions, we prove that every compact invariant set $\mathcal I$ of the semiflow generated by the semilinear damped wave equation u_{tt}+\alpha u_t+\beta(x)u-\Deltau = f(x,u), (t,x)\in[0,+\infty[\times\Omega, u = 0,…

We prove existence of global attractors for damped hyperbolic equations of the form $$\aligned \eps u_{tt}+\alpha(x) u_t+\beta(x)u- \sum_{ij}(a_{ij}(x) u_{x_j})_{x_i}&=f(x,u),\quad x\in \Omega, t\in[0,\infty[, u(x,t)&=0,\quad x\in \partial…

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

We address, in a three-dimensional spatial setting, both the viscous and the standard Cahn-Hilliard equation with a nonconstant mobility coefficient. As it was shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, one…

We prove existence of global attractors for parabolic equations of the form $$u_t+\beta(x)u-\sum_{ij}\partial_i(a_{ij}(x)\partial_j u)=f(x,u)$$ with Dirichlet boundary condition on an arbitrary unbounded domain $\Omega$ in $\R^3$, without…

The aim of this paper is studying the compact global attractors for non-autonomous lattice dynamical systems of the form $u_{i}'=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_{i}+f(u_i)+f_{i}(t)\ (i\in \mathbb Z,\ \lambda >0)$. We prove their…

Under consideration is the damped semilinear wave equation \[ u_{tt}+u_t-\Delta u + u + f(u)=0 \] on a bounded domain $\Omega$ in $\mathbb{R}^3$ with a perturbation parameter $\varepsilon>0$ occurring in an acoustic boundary condition,…

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.

The purpose of this paper is to investigate the existence and Hausdorff dimension as well as fractal dimension of global attractors for a delayed reaction-diffusion equation on an unbounded domain. The noncompactness of the domain causes…

We consider the nonlinear integrodifferential Benjamin-Bona-Mahony equation $$ u_t - u_{txx} + u_x - \int_0^\infty g(s) u_{xx}(t-s) {\rm d} s + u u_x = f $$ where the dissipation is entirely contributed by the memory term. Under a suitable…

This paper is concerned with the long-time behavior of solutions for the three dimensional primitive equations of large-scale ocean and atmosphere dynamics in an unbounded domain. Since the Sobolev embedding is no longer compact in an…

The paper investigates the existence of global attractors and their upper semicontinuity for a structural damped wave equation on $\mathbb{R}^{N}: u_{tt}-\Delta u+(-\Delta)^\alpha u_{t}+u_{t}+u+g(u)=f(x)$, where $\alpha\in (1/2, 1)$ is…

In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to…

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 this paper we consider the following nonlocal autonomous evolution equation in a bounded domain $\Omega$ in $\mathbb{R}^N$ \[ \partial_t u(x,t) =- h(x)u(x,t) + g \Big(\int_{\Omega} J(x,y)u(y,t)dy \Big) +f(x,u(x,t)) \] where $h\in…