F. Ortegón Gallego

Analysis and numerical simulation of an induction-conduction model arising in steel heat treating

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. We consider a mathematical model for the description of the heating-cooling industrial process of a steel workpiece. This model consists of a nonlinear coupled partial differential system of equations involving the electric potential, the magnetic vector potential, the temperature, together with a system of ordinary differential equations for the steel phase fractions. Due to the different time scales related to the electric potential and the magnetic vector potential versus the temperature, we introduce the harmonic regime, leading to a new system of nonlinear PDEs. Finally, we have carried out some 2D numerical simulations of this heating-cooling industrial process.

On certain doubly non-uniformly and singular non-uniformly elliptic systems

Abstract 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 zero, arising to a doubly non-uniformly elliptic system. In the second one, we assume in addition that the thermal conductivity blows up for a finite value of the temperature, arising to a singular and non-uniformly coupled system.

Duality and Weak Efficiency in Vector Variational Problems

We establish weak, strong, and converse duality results for weakly efficient solutions in vector or multiobjective variational problems, which extend and improve recent papers. For this purpose, we consider Kuhn–Tucker optimality conditions, weighting variational problems, and some classes of generalized convex functions, recently introduced, which are extended in this work. Furthermore, a related open question is discussed.

Analysis of a non-uniformly elliptic and nonlinear coupled parabolic–elliptic system arising in steel hardening

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 scales related to the electric potential and the magnetic vector potential versus the temperature. This lead us to a new system of nonlinear partial differential equations.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 scales related to the electric potential and the magnetic vector potential versus the temperature. This lead us to a new system of nonlinear partial differential equations.