María Teresa González Montesinos

Renormalized solutions to a nonlinear parabolic-elliptic system

The aim of this paper is to show the existence of renormalized solutions to a parabolic-elliptic 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.

Numerical Simulation of Potential Maxwell’s Equations in the Harmonic Regime

The aim of this work is to perform some numerical experiments for the resolution of a strongly coupled parabolic–elliptic system that describes the heating induction–conduction industrial process of a steel workpiece, whose unknowns are the electric potential, the magnetic vector potential, and the temperature. In order to make the numerical simulations lighter, and taking into account the different time scales between the potentials and the temperature, a new system of nonlinear partial differential equations (PDEs) has been constructed that describes the heating process in the harmonic regime.

Weak Solutions to a Nonuniformly Elliptic PDE System in the Harmonic Regime

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 L 1 in the energy balance equation, yields to a difficult theoretical situation. The existence result gives a weak solution to a similar PDEs system where the energy balance equation has been perturbed by a measure term.