Artículos (Matemática Aplicada I)
https://hdl.handle.net/11441/10894
2019-09-16T04:49:13ZThe thermistor problem with degenerate thermal conductivity and metallic conduction
https://hdl.handle.net/11441/89120
The thermistor problem with degenerate thermal conductivity and metallic conduction
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 practical interest of the
Wiedemann–Franz law with metallic conduction and lead us to very complex
mathematical situations.
2007-01-01T00:00:00ZRenormalized Solutions to a Nonlinear Parabolic-Elliptic System
https://hdl.handle.net/11441/89118
Renormalized Solutions to a Nonlinear Parabolic-Elliptic System
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.
2005-01-01T00:00:00ZOn certain doubly non-uniformly and singular non-uniformly elliptic systems
https://hdl.handle.net/11441/89117
On certain doubly non-uniformly and singular non-uniformly elliptic systems
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.
2003-09-01T00:00:00ZPartial Differential Equations: On the existence of solutions for a strongly degenerate system
https://hdl.handle.net/11441/89116
Partial Differential Equations: On the existence of solutions for a strongly degenerate system
We establish the existence of a solution in a certain sense to a strongly degenerate problem consisting in a coupled nonlinear
parabolic-elliptic system. The diffusion term in the parabolic equation is of the form − div a(x, t, u, ∇u), where a is an operator
of the Leray–Lions type. Moreover, the second equation is nonuniformly elliptic.; 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 − div a(x, t, u, ∇u), où a est un
opérateur du type de Leray–Lions. En outre, la seconde équation de ce système est non-uniformement elliptique.
2006-01-01T00:00:00Z