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A survey for the Muskat problem and a new estimate
(Springer, 2017-03)
This paper shows a summary of mathematical results about the Muskat problem. The main concern is well-posed scenarios which include the possible formation of singularities in finite time or existence of solutions for all ...
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Lineability criteria, with applications
(Elsevier, 2014-03-15)
Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed ...
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Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases
(American Mathematical Society, 2015-11)
Let B be a homothecy invariant collection of convex sets in Rn. Given a measure μ, the associated weighted geometric maximal operator MB,μ is defined by MB,μf(x) := sup x∈B∈B 1/μ(B) B |f|dμ. It is shown that, provided μ ...
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Komlós' Theorem and the Fixed Point Property for affine mappings
(American Mathematical Society, 2018-12)
Assume that X is a Banach space of measurable functions for which Koml´os’ Theorem holds. We associate to any closed convex bounded subset C of X a coefficient t(C) which attains its minimum value when C is closed for the ...
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Characterization of dual mixed volumes via polymeasures
(Elsevier, 2015-06-15)
We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated to it. To do this, we use tools from the theory of multilinear operators on spaces of continuos functions. ...
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Homogenization of an incompressible non-Newtonian flow through a thin porous medium
(Springer, 2017)
In this paper, we consider a non-Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically solid cylinders of size aε. The flow is described by the 3D incompressible Stokes system with a ...
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Derivation of a coupled Darcy-Reynolds equation for a fluid flow in a thin porous medium including a fissure
(Springer, 2017)
We study the asymptotic behavior of a fluid flow in a thin porous medium of thickness ε, which characteristic size of the pores ε, and containing a fissure of width ηε. We consider the limit when the size of the pores ...
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Analysis of the effects of a fissure for a non-Newtonian fluid flow in a porous medium
(International Press, 2018)
We study the solution of a non-Newtonian flow in a porous medium which characteristic size of the pores ε and containing a fissure of width ηε. The flow is described by the incompressible Stokes system with a nonlinear ...
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Asymptotic behaviour of the nonautonomous SIR equations with diffusion
(American Institute of Mathematical Sciences (AIMS), 2014)
The existence and uniqueness of positive solutions of a nonautonomous system of SIR equations with diffusion are established as well as the continuous dependence of such solutions on initial data. The proofs are facilitated ...
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The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium
(Springer, 2018)
We consider a Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size aε. Generalizing [2], the fluid is described by the 3D incompressible Navier-Stokes ...