52 citations · 130 across the 13 of their papers we have counts for
14 papers
Periodic Homogenization of Local/Nonlocal Systems
Marcone C. Pereira, Luiza C. Rosa da Silva, Julio D. Rossi
In this paper, we study the homogenization of elliptic equations that combine a local part, given by the Laplacian with Neumann boundary conditions, and its nonlocal version, defin…
Attractor Continuity for Semilinear Parabolic Equations on Thin Domains with Degenerating Outward Peaks
Elaine A. Tavares-Lima, Bianca Lorenzi, Marcone C. Pereira
In this work, we analyze the asymptotic behavior of the attractors associated with a semilinear parabolic equation subject to homogeneous Neumann boundary conditions and defined on…
Time-scale analysis non-local diffusion systems, applied to disease models
Marcone C. Pereira, Sergio Oliva, Larissa M. Sartori
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…
Nonlocal and nonlinear evolution equations in perforated domains
Marcone C. Pereira, Silvia Sastre-Gomez
In this work we analyze the behavior of the solutions to nonlocal evolution equations of the form with in a…
Concentrated reaction terms on the boundary of rough domains for a quasilinear equation
Ariadne Nogueira, Jean Carlos Nakasato, Marcone C. Pereira
In this work we analyze the solutions of a -Laplacian equation with homogeneous Neumann boundary conditions set in a family of rough domains with a nonlinear term concentrated o…
Nonlocal problems in perforated domains
Marcone C. Pereira, Julio D. Rossi
In this paper we analyze nonlocal equations in perforated domains. We consider nonlocal problems of the form with in a perforated doma…
Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries
José M. Arrieta, Ariadne Nogueira, Marcone C. Pereira
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 t…
Dynamical boundary conditions in a non-cylindrical domain for the Laplace equation
Pedro T. P. Lopes, Marcone C. Pereira
In this paper, we study existence, uniqueness and asymptotic behavior of the Laplace equation with dynamical boundary conditions on regular non-cylindrical domains. We write the pr…
Continuity of attractors for a family of perturbations of the square
Pricila S. Barbosa, Antônio L. Pereira, Marcone C. Pereira
We consider here the family of semilinear parabolic problems \begin{equation*} \begin{array}{rcl} \left\{ \begin{array}{rcl} u_t(x,t)&=&Δu(x,t) -au(x,t) + f(u(x,t)) ,\,\,\ x \in Ω_…
Parabolic problems in highly oscillating thin domains
Marcone C. Pereira
In this work we consider the asymptotic behavior of the nonlinear semigroup defined by a semilinear parabolic problem with homogeneous Neumann boundary conditions posed in a bounde…
Correctors for the Neumann problem in thin domains with locally periodic oscillatory structure
Marcone C. Pereira, Ricardo P. Silva
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…
A nonlinear elliptic problem with terms concentrating in the boundary
Gleiciane S. Aragão, Antônio L. Pereira, Marcone C. Pereira
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 i…
The Neumann problem in thin domains with very highly oscillatory boundaries
José M. Arrieta, Marcone C. Pereira
In this paper we analyze the behavior of solutions of the Neumann problem posed in a thin domain of the type $R^ε= \{(x_1,x_2) \in \R^2 \; | \; x_1 \in (0,1), \, - \, ε\, b(x_1) <…
Homogenization in a thin domain with an oscillatory boundary
José M. Arrieta, Marcone C. Pereira
In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type $R^ε= \{(x,y) \in \R^2; x \in (0,1), 0 < y < εG(x, x/ε)\…