Correctors for the Neumann problem in thin domains with locally periodic oscillatory structure

In this paper we are concerned with convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain exhibiting highly oscillatory behavior in part of its boundary. We deal with the resonant case in which the height, amplitude and period of the oscillations are all of the same order which is given by a small parameter $\epsilon > 0$. Applying an appropriate corrector approach we get strong convergence when we replace the original solutions by a kind of first-order expansion through the Multiple-Scale Method.Comment: to appear in Quarterly of Applied Mathematic

Time-scale analysis non-local diffusion systems, applied to disease models

The objective of the present paper is to use the well known Ross-Macdonald models as a prototype, incorporating spatial movements, identifying different times scales and proving a singular perturbation result using a system of local and non-local diffusion. This results can be applied to the prototype model, where the vector has a fast dynamics, local in space, and the host has a slow dynamics, non-local in space

Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries

In this work we study the behavior of a family of solutions of a semilinear elliptic equation, with homogeneous Neumann boundary condition, posed in a two-dimensional oscillating thin region with reaction terms concentrated in a neighborhood of the oscillatory boundary. Our main result is concerned with the upper and lower semicontinuity of the set of solutions. We show that the solutions of our perturbed equation can be approximated with ones of a one-dimensional equation, which also captures the effects of all relevant physical processes that take place in the original problem

A nonlinear elliptic problem with terms concentrating in the boundary

In this paper we investigate the behavior of a family of steady state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a $\epsilon$-neighborhood of a portion $\Gamma$ of the boundary. We assume that this $\epsilon$-neighborhood shrinks to $\Gamma$ as the small parameter $\epsilon$ goes to zero. Also, we suppose the upper boundary of this $\epsilon$-strip presents a highly oscillatory behavior. Our main goal here is to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on $\Gamma$, which depends on the oscillating neighborhood

Comparison of European stone fruit yellows phytoplasma strains differing in virulence by multi-gene sequence analyses

Twenty strains of the ESFY phytoplasma, which on the basis of graft-inoculation experiments greatly differ in aggressiveness, were examined by sequence analyses of several PCR-amplified non-ribosomal genes in order to identify molecular markers linked to virulence. These strains, which were maintained in P. insititia rootstock St. Julien GF 655/2 were indistinguishable with techniques for routine phytoplasma differentiation and characterization such as sequence and RFLP analyses of PCR-amplified rDNA. Also, the virulent ESFY strains maintained in periwinkle, namely GSFY1, GSFY2 and ESFY1, as well as an avirulent strain of the same phytoplasma, maintained in apricot, which was identified in recovered apricot trees in France and used there as a cross protecting agent, were included in the work for comparison. For PCR amplification, primers were designed from a number of genes distributed over the chromosome of the closely related apple proliferation phytoplasma strain AT. Visible PCR products were only obtained with primer pairs derived from the tuf gene which encodes the elongation factor Tu (EF-Tu), rpsC (rps3) gene encoding the ribosomal protein S3, tlyC gene which encodes a hemolysin known as a membrane-damaging agent and important virulence factor of many bacteria, the imp and fol genes encoding an immunodominant membrane protein and an enzyme involved in the folate biosynthesis, respectively. Nucleotide sequence comparisons revealed that the highest genomic variability occurred within the imp gene sequence with dissimilarity values ranging from 0.2 to 4.6%. For the remaining genes, the strains examined proved to be identical or nearly identical. Within the tuf gene, an extra TaqI site known to occur in strain GSFY1 was not identified in other strains. The genetic differences observed among the strains examined are neither suitable markers for strain differentiation nor linked to pathological traits.Keywords: European stone fruit yellows, strain virulence, 16SrX group, tlyC gene, Prunus spp

Error estimates for a Neumann problem in highly oscillating thin domains

In this work we analyze convergence of solutions for the Laplace operator with Neumann boundary conditions in a two-dimensional highly oscillating domain which degenerates into a segment (thin domains) of the real line. We consider the case where the height of the thin domain, amplitude and period of the oscillations are all of the same order, given by a small parameter $\epsilon$. We investigate strong convergence properties of the solutions using an appropriate corrector approach. We also give error estimates when we replace the original solutions for the second-order expansion through the Multiple-Scale Method