ROJAS MEDAR , Marko Antonio

An iterative method is proposed for nding approximate solutions of an initial and boundary value problem for a nonstationary generalized Boussinesq model for thermally driven convection of fluids with temperature dependent viscosity and thermal conductivity. Under certain conditions, it is proved that such approximate solutions converge to a...

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In this work, we consider an optimal control problem for the generalized bioconvective flow, which is a well known model to describe the convection caused by the concentration of upward swimming microorganisms in a fluid. Firstly, we study the existence and uniqueness of weak solutions for this model, moreover we prove the existence of the...

We study the equivalence between the solutions of the variational-like inequality problem and the solutions of certain nonsmooth and nonconvex vectorial optimization problem.

The Navier-Stokes- equations belong to the family of LES (Large Eddy Simulation) models whose fundamental idea is to capture the influence of the small scales on the large ones without computing all the whole range present in the flow. The constant is a regime flow parameter that has the dimension of the smallest scale being resolvable by...

An optimal error estimate of the numerical velocity, pressure and angular velocity, is proved for the fully discrete penalty finite element method of the micropolar equations, when the parameters ², ∆t and h are sufficiently small. In order to obtain above we present the time discretization of the penalty micropolar equation which is based on...

We prove existence of a global weak solution for a nematic liquid crystal problem by means of a penalization method using a simplified Ericksen-Leslie model and a new compactness property for the gradient of the director field.

Dans ce papier, on analyse un problème de valeurs initiales et valeurs aux limites pour un système d'équations aux dérivées partielles qui modélise le flux instationnaire d'un fluide asymmétrique incompressible non homogène. Sous des conditions similaires aux conditions usuellement imposées aux équations tridimensionelles de Navier-Stokes non...

We consider an optimal control problem governed by a system of nonlinear partial differential equations modelling viscous incompressible flows submitted to variations of temperature. We use a generalized Boussinesq approximation. We obtain the existence of the optimal control as well as first order optimality conditions of Pontryagin type by...

We consider the existence and uniqueness of periodic solutions for the generalized bioconvective flow, which is a well known model to describe the convection caused by the concentration of upward swimming microorganism in a fluid.

Varios trabajos relacionados con la existencia y unicidad de soluciones para ecuaciones diferenciales difusas son basados en que el problema de Cauchy es equivalente a una ecuación integral. Este hecho que también es verdadero en el contexto clásico, no es siempre verdadero en el contexto de ecuaciones diferenciales difusas donde la derivada es...

We treat the existence of reproductive solution (weak periodic solution) of a second-grade fluid system in two dimensions, by using the Galerkin approximation method and compactness arguments.

We consider the initial boundary value problem for the system of equations describing the nonstationary flow of an incompressible micropolar fluid in a domain Ω of R3.Under hypotheses that are similar to the Navier-Stokes equations ones, by using an iterative scheme, we prove the existence and uniqueness of strong solution in Lp(Ω), for p > 3.

En este trabajo diremos cómo se pueden modelar ciertos sistemas tomados de la realidad que usan conceptos propios de la Matemática Difusa (conjuntos, multifunciones e inclusiones diferenciales "fuzzy"). Consideraremos problemas de valor inicial para inclusiones diferenciales "fuzzy" y analizaremos la existencia de solución local. También...

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If x∗ is a local minimum solution, then there exists a ball of radius r > 0 such that f (x) ≥ f (x∗) for all x ∈ B(x∗,r). The purpose of the current study is to identify the suitable B(x∗,r) of the local optimal solution x∗ for a particular multiobjective optimization problem. We provide a way to calculate the largest radius of the ball...

We study a class of abstract nonlinear equations in a separable Hilbert space for which we prove properties of the set of solutions. The results apply, in particular, in several models of hydrodynamics, such as magneto-micropolar equations, micropolar fluid equations, Boussinesq and Navier-Stokes equations.

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Le but principal de ce travail est d'étudier le concept de solution très faible pour le système de Stokes hydrostatique avec conditions aux limites mixtes (condition de Neumann non régulière sur la surface rigide et condition de Dirichlet homogène dans le reste). Dans le cas du problème de Stokes, ce sujet a été étudié par Conca [Rev. Mat. Apl....

In [3] L. C. Berselli, On a Regularity Criterion for the Solutions to the 3D Navier-Stokes Equations, Diff. and Integral Eq., Vol. 15, Number 9, 1129-1137 (2002). , L. Berselli showed that the additional regularity hypothesis for the velocity gradient ∇u ∈ L 2q 2q−3 (0, T;L q (Ω)), for some q ∈ (3/2, +∞], implies the strong regularity for the...

In this article, our aims is to review some of the results that are currently available concerning the existence, uniqueness and regularity of reproductive and time periodic solutions of the Navier-Stokes equations and some variants. By the way, we present some open problems.

In this paper we prove existence of weak solution with the reproductivity in time property, for a penalized PDE's system related to a nematic liquid crystal model. This problem is relatively explicit when time-independent Dirichlet bound- ary conditions are imposed for the orientation of crystal molecules. Neverthe- less, for the time-dependent...

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In this article, our aims is to review some of the results that are currently available concerning the existence, uniqueness and regularity of reproductive and time periodic solutions of the Navier-Stokes equations and some variants. By the way, we present some open problems.