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Last name: ORTEGÓN GALLEGO
First name: Francisco
El presente trabajo trata sobre el estudio de un modelo matemático de Turbulencia: el modelo M.P.P.Este Modelo fue propuesto por McLaughin, Papanicolaou y Pironneau ([27]) en u n intento de demostrar la hipótesis de Reynolds (dependencia del tensor de Rey
The aim of this work is to establish the existence of a capacity solution to the thermistor problem supposing that the thermal and the electrical conductivities are not bounded below by a positive constant value. Furthermore, the thermal conductivity vanishes at points where the temperature is null. These assumptions on data include the case of...
We consider the steady state of the thermistor problem consisting of a coupled set of nonlinear elliptic equations governing the temperature and the electric potential. We study the existence of weak solutions under two kind of assumptions. The first one considers the case in which the two diffusion coefficients are not bounded below far from...
We study the existence of weak solutions to a nonlinear coupled parabolic–elliptic system arising in the heating industrial process of a steel workpiece. The unknowns are the electric potential, the magnetic vector potential and the temperature. The different time scales related to the electric potential and the magnetic vector potential versus...
Sur l'existence de solutions pour un système fortement dégénéré. On montre l'existence d'une solution dans un certain sens d'un problème fortement dégénéré constitué par un système non-linéaire de deux équations aux dérivées partielles couplées du type parabolique-elliptique, le terme de diffusion de l'équation parabolique étant de la forme −...
Nous étudions un système non-linéaire d'équations du type parabolique provenant de la modélisation de la turbulence. Les inconnues sont les N composantes du champ des vitesses u couplées avec deux grandeurs scalaires θ et ϕ. Ce système présente un terme de diffusion non-linéaire sous forme matricielle A(θ,ϕ) et les termes sources non-linéaires...
The aim of this paper is to show the existence of renormalized solutions to a parabolicelliptic system with unbounded diffusion coefficients. This system may be regarded as a modified version of the well-known thermistor problem; in this case, the unknowns are the temperature in a conductor and the electrical potential.
The goal of this work is to analyse the existence of weak solutions to a coupled nonlinear parabolic–elliptic system derived from the heating industrial process of a steel workpiece, and whose unknowns are the electric potential, the magnetic vector potential and the temperature. We introduce the harmonic regime because of the different time...
We study the existence of weak solutions to a nonlinear strongly coupled parabolic–elliptic PDEs arising in the heating induction-conduction process of steel hardening. In this setting, our major concern is to consider the case when the electric conductivity is nonuniformly elliptic which, together with a right hand side in L1 in the energy...
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En este trabajo se aborda la resolución numérica del problema del termistor en dimensión dos. La mayor dificultad de dicho an´alisis reside en el hecho que se supone conducción metálica y además se satisface la ley de Wiedemann–Franz. Para la simulación numérica se ha considerado el caso de un termistor PTC de medida o silistor. En tal caso,...
The goal of steel heat treating is to create a hard enough part over certain critical surfaces or volumes of the workpiece and at the same time keeping its ductility properties all over the rest of the workpiece. Weconsider a mathematical model for the description of the heating–cooling industrial process of a steel workpiece. This model...
El acero es una aleación de hierro y carbono al que se pueden unir una serie de elementos aleantes (Si, Mn, Ni, Cr, Al,. . . ). La cantidad de cada uno de ellos determina las propiedades del material y, por tanto, sus usos y aplicaciones industriales. En los aceros hipoeutectoides (con un nivel de C inferior al 0'77 %), se aprecia un cambio...
This paper summarizes a mathematical model for the industrial heating and cooling processes of a steel workpiece corresponding to the steering rack of an automobile. The general purpose of the heat treatment process is to create the necessary hardness on critical parts of the workpiece. Hardening consists of heating the workpiece up to a...
We describe a mathematical model for the industrial heating and cooling processes of a steel workpiece representing the steering rack of an automobile. The goal of steel heat treating is to provide a hardened surface on critical parts of the workpiece while keeping the rest soft and ductile in order to reduce fatigue. The high hardness is due...