52 citations · 249 across the 15 of their papers we have counts for
17 papers
Elliptic and parabolic problems in thin domains with doubly weak oscillatory boundary
José M. Arrieta, Manuel Villanueva-Pesqueira
In this work we consider higher dimensional thin domains with the property that both boundaries, bottom and top, present oscillations of weak type. We consider the Laplace operator…
Bifurcation and hyperbolicity for a nonlocal quasilinear parabolic problem
José M. Arrieta, Alexandre N. Carvalho, Estefani M. Moreira +1
In this article, we study a one-dimensional nonlocal quasilinear problem of the form , with Dirichlet boundary conditions on the interval $[0,π…
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…
The p-Laplacian equation in thin domains: The unfolding approach
José Maria Arrieta, Jean Carlos Nakasato, Marcone Corrêa Pereira
In this work we apply the unfolding operator method to analyze the asymptotic behavior of the solutions of the -Laplacian equation with Neumann boundary condition set in a bound…
Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains
José M. Arrieta, Francesco Ferraresso, Pier Domenico Lamberti
We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thi…
Distance of attractors for thin domains
José M. Arrieta, Esperanza Santamaría
In this work we consider a dissipative reaction-diffusion equation in a -dimensional thin domain shrinking to a one dimensional segment and obtain good rates for the convergence…
-Estimates on the distance of Inertial Manifolds
José M. Arrieta, Esperanza Santamaría
In this paper we obtain -estimates on the distance of inertial manifolds for dynamical systems generated by evolutionary parabolic type equations. We consider the situatio…
Boundary homogenization for a triharmonic intermediate problem
José Arrieta, Francesco Ferraresso, Pier Domenico Lamberti
We consider the triharmonic operator subject to homogeneous boundary conditions of intermediate type on a bounded domain of the N-dimensional Euclidean space. We study its spectral…
Higher order elliptic operators on variable domains. Stability results and boundary oscillations for intermediate problems
José M. Arrieta, Pier Domenico Lamberti
We study the spectral behavior of higher order elliptic operators upon domain perturbation. We prove general spectral stability results for Dirichlet, Neumann and intermediate boun…
Unfolding operator method for thin domains with a locally periodic highly oscillatory boundary
José M. Arrieta, Manuel Villanueva-Pesqueira
We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillati…
Estimates on the distance of inertial manifolds
José M. Arrieta, Esperanza Santamaría
In this paper we obtain estimates on the distance of inertial manifolds for dynamical systems generated by evolutionary parabolic type equations. We consider the situation where th…
Thin domains with doubly oscillatory boundary
José M. Arrieta, Manuel Villanueva-Pesqueira
We consider a 2-dimensional thin domain with order of thickness ε which presents oscillations of amplitude also ε on both boundaries, top and bottom, but the period of the oscillat…
Stability estimates in for solutions of elliptic equations in varying domains
José M. Arrieta, Gerassimos Barbatis
We consider second-order uniformly elliptic operators subject to Dirichlet boundary conditions. Such operators are considered on a bounded domain and on the domain resul…
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)\…
Approximating travelling waves by equilibria of non local equations
Jose M. Arrieta, Maria Lopez-Fernandez, Enrique Zuazua
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non l…
Geometric versus spectral convergence for the Neumann Laplacian under exterior perturbations of the domain
Jose M. Arrieta, David Krejcirik
We analyze the behavior of the eigenvalues and eigenfunctions of the Laplace operator with homogeneous Neumann boundary conditions when the domain is perturbed. We focus on exterio…