Pullback attractors for the non-autonomous complex Ginzburg–Landau type equation with p-Laplacian

In this paper, we are concerned with the long-time behavior of the non-autonomous complex Ginzburg–Landau type equation with p-Laplacian. We first prove the existence of pullback absorbing sets in L2(Ω)∩W01,p(Ω)∩Lq(Ω) for the process {U(t,τ)}t⩾τ corresponding to the non-autonomous complex Ginzburg–Landau type equation with p-Laplacian. Next, the existence of a pullback attractor in L2(Ω) is established by the Sobolev compactness embedding theorem. Finally, we prove the existence of a pullback attractor in W01,p(Ω) for the process {U(t,τ)}t⩾τ by asymptotic a priori estimates

Trajectory and global attractors for generalized processes

In this work the theory of generalized processes is used to describe the dynamics of a nonautonomous multivalued problem and, through this approach, some conditions for the existence of trajectory attractors are proved. By projecting the trajectory attractor on the phase space, the uniform attractor for the multivalued process associated to the problem is obtained and some conditions to guarantee the invariance of the uniform attractor are given. Furthermore, the existence of the uniform attractor for a class of p-Laplacian nonautonomous problems with dynamical boundary conditions is established.Conselho Nacional de Desenvolvimento Científico e Tecnológico. BrasilEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Ministerio de Economía y Competitividad (MINECO). EspañaJunta de Andalucí

Asymptotic behaviour of the non-autonomous 3D Navier-Stokes problem with coercive force

We construct pullback attractors to the weak solutions of the three-dimensional Dirichlet problem for the incompressible Navier-Stokes equations in the case when the external force may become unbounded as time goes to plus or minus infinity.Comment: 22 page

Bi-space pullback attractors for closed processes

nuloIn the description of the long-time behavior of solutions to nonautonomous differential equations the notion of a pullback attractor plays a similar role as the global attractor in autonomous dynamical systems. We present the theorem on the existence of a pullback attractor if the evolution process is a family of closed operators. The abstract result is formulated in the context of the smoothing properties of the process and for pullback attractors attracting a given universe, i.e. a chosen class of possibly time-dependent families of sets. We also present an application of the result to reaction-diffusion equations

Coupled nonautonomous inclusion systems with spatially variable exponents

A family of nonautonomous coupled inclusions governed by p(x)-Laplacian operators with large diffusion is investigated. The existence of solutions and pullback attractors as well as the generation of a generalized process are established. It is shown that the asymptotic dynamics is determined by a two dimensional ordinary nonautonomous coupled inclusion when the exponents converge to constants provided the absorption coefficients are independent of the spatial variable. The pullback attractor and forward attracting set of this limiting system is investigated

An exponential growth condition in H^2 for the pullback attractor of a non-autonomous reaction-diffusion equation

Some exponential growth results for the pullback attractor of a reaction-diffusion when time goes to ¡1 are proved in this paper. First, a general result about Lp\H1 0 exponential growth is established. Then, under additional assumptions, an exponential growth condition in H2 for the pullback attractor of the non-autonomous reaction-diffusion equation is also deduced

Global attractors for multivalued semiflows with weak continuity properties

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 semilinear source term is presented.Comment: to appear in Nonlinear Analysis Series A, Theory, Methods & Application