María Anguiano

EXISTENCE OF PULLBACK ATTRACTOR FOR A REACTION–DIFFUSION EQUATION IN SOME UNBOUNDED DOMAINS WITH NON-AUTONOMOUS FORCING TERM IN H-1

The existence of a pullback attractor in L2(Ω) for the following non-autonomous reaction–diffusion equation

The ε-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors

\left\{ \begin{array}{@{}l@{\quad}l@{}}% \displaystyle\frac{\partial u}{\partial t}-\bigtriangleup u=f(u)+h(t), &\text{in}\Omega\times(\tau,+\infty),\\[15pt] u=0, &\text{on}\partial\Omega\times(\tau,+\infty), \\[8pt] u(x,\tau)=u_{\tau}(x), xH^{-1} (\Omega))

Pullback Attractors for a Reaction–Diffusion Equation in a General Nonempty Open Subset of ℝN with Nonautonomous Forcing Term in H−1

. The main concept used in the proof is the asymptotic compactness of the process generated by the problem.

Attractors for a Nonautonomous Liénard Equation

We study a nonautonomous reaction-diffusion equation with zero Dirichlet boundary condition, in an unbounded domain containing a nonautonomous forcing term taking values in the space H −1, and with a continuous nonlinearity which does not ensure uniqueness of solution. Using results of the theory of set-valued nonautonomous (pullback) dynamical systems, we prove the existence of minimal pullback attractors for this problem. We ensure that the pullback attractors are connected and also establish the relation between these attractors.

PULLBACK ATTRACTORS FOR A NONAUTONOMOUS INTEGRO-DIFFERENTIAL EQUATION WITH MEMORY IN SOME UNBOUNDED DOMAINS

We prove an estimation of the Kolmogorov \begin{document}

Pullback attractor for a non-autonomous reaction-diffusion equation in some unbounded domains

\varepsilon

Pullback attractors for reaction-diffusion equations in some unbounded domains with an H-1 -valued non-autonomous forcing term and without uniqueness of solutions

\end{document} -entropy in \begin{document}

H2-boundedness of the pullback attractor for a non-autonomous reaction–diffusion equation

H

Pullback attractors for non-autonomous reaction–diffusion equations with dynamical boundary conditions

\end{document} of the unitary ball in the space \begin{document}