相关论文: Global Attractor of a coupled Two-Cell Brusselator…

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…

The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a…

We consider the initial value problem for the semilinear plate equation with nonlocal nonlinearity. We prove the existence of global attractor and then establish the regularity and finite dimensionality of this attractor.

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 article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading…

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…

We prove existence of the global attractor of the damped and driven Euler--Bardina equations on the 2D sphere and on arbitrary domains on the sphere and give explicit estimates of its fractal dimension in terms of the physical parameters.

The existence of global attractors is investigated for the Signorini problem with pointwise dissipation. It is shown that both the semilinear Signorini problem and the elastic obstacle problem with normal compliance exhibit exponential…

We study the existence and uniqueness of a bounded weak solution for a triply nonlinear thermistor problem in Sobolev spaces. Furthermore, we prove the existence of an absorbing set and, consequently, the universal attractor.

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 $…

We consider a nonlinear reaction-diffusion equation settled on the whole euclidean space. We prove the well-posedness of the corresponding Cauchy problem in a general functional setting, namely, when the initial datum is uniformly locally…

In this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The basin of the global attractor exhibits historic behaviour…

We consider a Large Eddy Simulation model for a homogeneous incompressible Newtonian fluid in a box space domain with periodic boundary conditions on the lateral boundaries and homogeneous Dirichlet conditions on the top and bottom…

A method is proposed to deal with some multivalued semiflows with weak continuity properties. An application to the reaction-diffusion problems with nonmonotone multivalued semilinear boundary condition and nonmonotone multivalued…

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…

A class of dissipative dynamical systems evolving on smooth constraint hypersurfaces endowed with degenerate induced bilinear forms is studied. The intrinsic evolution is generated by constraint--preserving vector fields on manifolds whose…

The Penrose-Fife system for phase transitions is addressed. Dirichlet boundary conditions for the temperature are assumed. Existence of global and exponential attractors is proved. Differently from preceding contributions, here the energy…

We consider a deconvolution model for 3D periodic flows. We show the existence of a global attractor for the model.

We study the asymptotic behavior of solutions of one coupled PDE-ODE system arising in mathematical biology as a model for the development of a forest ecosystem. In the case where the ODE-component of the system is monotone, we establish…

The aim of this work is to examine the upper-semicontinuity properties of the family of global attractors admitted by a non-isothermal viscous relaxation of some nonlocal Cahn-Hilliard equations. We prove that the family of global…