and Applied Analysis 3 In 15 the asymptotic behavior of 1.1 was studied and it was proven the existence of a global attractor for the semigroup associated to 1.1 , that is, the semigroup of operators defined as S t : u0 ∈ H −→ u t ∈ H, 1.4 The main tool in proving the existence of a global attractor is to show the existence of an absorbing set inH2 I see Theorem 1.1 in 1 . Theorem 1.1 see 15 . ...

We study the nonlinear dynamics of a reaction-diffusion equation where the nonlinearity presents a discontinuity. We prove the upper semicontinuity of solutions and of the global attractor with respect to smooth approximations of the nonlinear term. We also give a complete description of the set of fixed points and study their stability. Finally, we analyze the existence of heteroclinic connect...

Abstract We present a systematic way to construct dynamical systems with a specific symmetry group G. Each symmetric strange attractor has a unique image attractor that is locally identical to it but different at the global topological level. Image attractors can be lifted to many inequivalent covering attractors. These are distinguished by an index that has related topological, algebraic and g...

We consider the solutions lying on the global attractor of the two-dimensional Navier–Stokes equations with periodic boundary conditions and analytic forcing. We show that in this case the value of a solution at a finite number of nodes determines elements of the attractor uniquely, proving a conjecture due to Foias and Temam. Our results also hold for the complex Ginzburg–Landau equation, the ...

We consider the global attractor of the critical SQG semigroup S(t) on the scale-invariant space H(T). It was shown in [15] that this attractor is finite dimensional, and that it attracts uniformly bounded sets in H(T) for any δ > 0, leaving open the question of uniform attraction in H(T). In this paper we prove the uniform attraction in H(T), by combining ideas from DeGiorgi iteration and nonl...

In this paper, we estimate the dimension of a global attractor for a nonclassical hyperbolic equation with a viscoelastic damping term in Hilbert spaces H2 0 × L2 and D(A) × H2 0 , where D(A) = {v ∈ H2 0 | Av ∈ L2} and A = ∆2. We obtain an explicit formula of the upper bound of the dimension of the attractor. The obtained dimension decreases as damping grows and is uniformly bounded for large d...