Asymptotic behavior of a reaction-diffusion problem with delay and reaction term concentrated in the boundary

In this work we analyze the asymptotic behavior of the solutions of a reaction-diffusion problem with delay when the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter goes to zero. This analysis of the asymptotic behavior uses, as a main tool, the convergence result found in [3]. Here, we prove the existence of a family of global attractors and that this family is upper semicontinuous at = 0. We also prove the continuity of the set of equilibria at = 0. 

Mathematical model with fractional order derivatives for Tuberculosis taking into account its relationship with HIV/AIDS and Diabetes

In this paper, we present a mathematical model for the study of resistance to tuberculosis treatment using fractional derivatives in the Caputo sense. This model takes into account the relationship between Tuberculosis, HIV/AIDS, and diabetes and differentiates resistance cases into MDR-TB (multidrug-resistant tuberculosis) and XDR-TB (extensively drug-resistant tuberculosis). We present the basic results associated with the model and study the behavior of the disease-free equilibrium points in the different sub-populations, TB-Only, TB-HIV/AIDS, and TB-Diabetes. We performed computational simulations for different fractional orders (α-values) using an Adams-Bashforth-Moulton type predictor-corrector PECE method. Among the results obtained, we have that the MDR-TB cases in all sub-populations decrease at the beginning of the study for the different α-values. In XDR-TB cases in the TB-Only sub-population, there is a decrease in the number of cases. XDR-TB cases in the TB-HIV/AIDS sub-population have differentiated behavior depending on α. This knowledge helps to design an effective control strategy. The XDR-TB cases in diabetics increased throughout the study period and outperformed all resistant compartments for the different α-values. We recommend special attention to the control of this compartment due to this growth

Reaction-diffusion systems on domains with thin channels

Ph.D.Jack K. Hal

Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary

In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction-diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter epsilon goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. (C) 2012 Elsevier Inc. All rights reserved.CAPES-BrazilCAPES (Brazil

An extension problem related to the square root of the Laplacian with Neumann boundary condition

In this work we define the square root of the Laplacian operator with Neumann boundary condition via harmonic extension method. By using Fourier series and periodic even extension we define the non-local operator square root in three type of bounded domains such as an interval, square or a ball. Also, as application we study the existence of weak solutions for a class of nonlinear elliptic problems

A discretization scheme for an one-dimensional reaction-diffusion equation with delay and its dynamics

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation

La Biennale di Venezia 49 : Esposizione Internazionale d’Arte

This two volume catalogue for the 49th Venice Biennale, the major theme of which is represented by the phrase “Plateau of Humankind,” features the work of artists from 64 countries and texts by more than 175 authors. The first volume includes a curatorial essay by Szeemann, and documentation of selected works. The second volume focuses on the work of artists who were chosen to represent the countries participating in the biennial. List of works. List of illustrations. Bio-bibliography 159 p. 19 bibl. ref