David Gómez-Castro

Homogenization of variational inequalities of Signorini type for the p-Laplacian in perforated domains when p ∈ (1, 2)

The asymptotic behavior, as ε → 0, of the solution uε to a variational inequality with nonlinear constraints for the p-Laplacian in an ε-periodically perforated domain when p ∈ (1, 2) is studied.

Linear diffusion with singular absorption potential and/or unbounded convective flow: The weighted space approach

In this paper we prove the existence and uniqueness of very weak solutions to linear diffusion equations involving a singular absorption potential and/or an unbounded convective flow on a bounded open set of

On the Effectiveness of Wastewater Cylindrical Reactors: an Analysis Through Steiner Symmetrization

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The Effectiveness Factor of Reaction-Diffusion Equations: Homogenization and Existence of Optimal Pellet Shapes

. In most of the paper we consider homogeneous Dirichlet boundary conditions but we prove that when the potential function grows faster than the distance to the boundary to the power -2 then no boundary condition is required to get the uniqueness of very weak solutions. This result is new in the literature and must be distinguished from other previous results in which such uniqueness of solutions without any boundary condition was proved for degenerate diffusion operators (which is not our case). Our approach, based on the treatment on some distance to the boundary weighted spaces, uses a suitable regularity of the solution of the associated dual problem which is here established. We also consider the delicate question of the differentiability of the very weak solution and prove that some suitable additional hypothesis on the data is required since otherwise the gradient of the solution may not be integrable on the domain.

Characterizing the strange term in critical size homogenization: quasilinear equations with a general microscopic boundary condition

The mathematical analysis of the shape of chemical reactors is studied in this paper through the research of the optimization of its effectiveness

Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles

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Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis “nano-composite” membranes

η such as introduced by R. Aris around 1960. Although our main motivation is the consideration of reactors specially designed for the treatment of wastewaters our results are relevant also in more general frameworks. We simplify the modeling by assuming a single chemical reaction with a monotone kinetics leading to a parabolic equation with a non-necessarily differentiable function. In fact we consider here the case of a single, non-reversible catalysis reaction of chemical order