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Artículo
Modelos matemáticos en biología: un viaje de ida y vuelta
(Sociedad Española de Matemática Aplicada, 2006)
El objetivo de este trabajo es mostrar la provechosa interacción entre la Biología y la Matemática. Para ello veremos cómo, por una parte, la Matemática es una herramienta sumamente interesante para entender distintos ...
Artículo
The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces
(National Academy of Sciences, 2009-07-07)
For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible Euler equation, we prove existence locally in time when the Rayleigh-Taylor condition is initially ...
Artículo
Analytical behavior of two-dimensional incompressible flow in porous media
(AIP Publishing (American Institute of Physics), 2007-06)
In this paper we study the analytic structure of a two-dimensional mass balance equation of an incompressible fluid in a porous medium given by Darcy’s law. We obtain local existence and uniqueness by the particle-trajectory ...
Artículo
Incompressible flow in porous media with fractional diffusion
(IOP Publishing, 2009-08)
In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy’s law. We show formation of singularities with infinite energy and for finite ...
Artículo
A maximum principle for the Muskat problem for fluids with different densities
(Springer, 2009-03)
We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy’s law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two ...
Artículo
Existence for the α-patch model and the QG sharp front in Sobolev spaces
(Elsevier, 2008-04-01)
We consider a family of contour dynamics equations depending on a parameter α with 0<α⩽1. The vortex patch problem of the 2-D Euler equation is obtained taking α→0, and the case α=1 corresponds to a sharp front of the QG ...
Artículo
A continuation method for weakly contractive mappings under the interior condition
(Hindawi, 2009)
Recently, Frigon proved that, for weakly contractive maps, the property of having a fixed point is invariant by a certain class of homotopies, obtaining as a consequence a Leray-Schauder alternative for this class of maps ...
Artículo
Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
(Springer, 2009-06)
A well known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1, 1) with respect to a couple of weights (w, Mw). In this paper we consider a somewhat “dual” ...
Artículo
A new characterization of the Muckenhoupt Ap weights through an extension of the Lorentz-Shimogaki theorem
(Indiana University, 2007)
Given any quasi-Banach function space X over Rn it is defined an index αX that coincides with the upper Boyd index αX when the space X is rearrangement-invariant. This new index is defined by means of the local maximal ...
Artículo
New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory
(Elsevier, 2009-03-01)
A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller that the m-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control ...