Jacson Simsen

Some Properties for Exact Generalized Processes

In this work, we define an exact generalized process and we establish some results such as monotonicity, compactness, and upper semicontinuity for the multivalued process defined by the exact generalized process. The main result is on compactness, invariance, and attraction properties of \(\omega \)-limit sets.

Characterization of Pullback Attractors for Multivalued Nonautonomous Dynamical Systems

In this paper we provide a review of the general results on pullback attractors for multivalued nonautonomous dynamical systems, completing at the same time some gaps in the theory. Also, when the attraction of a class of families of sets rather than just bounded sets is considered, we obtain the characterization of the pullback attractor as the union of all complete trajectories belonging to this class. Finally, an application to a reaction-diffusion equation without uniqueness of solutions is given.

On

In this work we prove continuity of solutions with respect to initial conditions and exponent parameters and we prove upper semicontinuity of a family of global attractors for problems of the form ∂us ∂t − div(|∇us|s∇us) + f(x, us) = g, where f : Ω×R→ R is a non-globally Lispchitz Carathéodory mapping, g ∈ L2(Ω), Ω is a bounded smooth domain in Rn, n ≥ 1 and ps(·)→ p in L∞(Ω) (p > 2 constant) as s goes to infinity.

p_s(x)

We study the asymptotic behavior of parabolic p(x)-Laplacian problems of the form ∂uλ ∂t − div(D|∇uλ|∇uλ) + a|uλ|uλ = B(uλ) in L(R), where n ≥ 1, p ∈ L∞(Rn) such that 2 M ≥ D(x) ≥ σ > 0 a.e. in R, λ ∈ [0,∞), B : L(R) → L(R) is a globally Lipschitz map and a : R → R is a non-negative continuous function such that there exists R1 > 0 with {x ∈ R; a(x) = 0} ⊂ BR1(0), infx∈Rn\BR1 (0) a(x) > 0, and ∫ R\BR1 (0) 1 a(x)2/(p(x)−2) dx < +∞. We also study the sensitivity of the problem according to the variation of the diffusion coefficients.

-Laplacian Parabolic Problems with Non-Globally Lipschitz Forcing Term

In this work we improve the result presented by Kloeden-Simsen-Stefanello Simsen in [ 8 ] by reducing uniform conditions. We prove theoretical results in order to establish convergence in the Hausdorff semi-distance of the component subsets of the pullback attractor of a non-autonomous multivalued problem to the global attractor of the corresponding autonomous multivalued problem.