Francisco Ortegon Gallego, Mohamed Rhoudaf, Hajar Sabiki
Abstract:
The existence of a capacity solution to the thermistor problem in the
context of inhomogeneous Musielak-Orlicz-Sobolev spaces is analyzed.
This is a coupled parabolic-elliptic system of nonlinear PDEs whose
unknowns are the temperature inside a semiconductor material,
,
and the electric potential,
.
We study the general case where the nonlinear elliptic operator in the
parabolic equation is of the form
, A being a Leray-Lions operator
defined on
, where M is a generalized N-function.
Submitted December 26, 2017. Published June 15, 2018.
Math Subject Classifications: 35J70, 35K61, 46E30, 35M13.
Key Words: Parabolic-elliptic system; Musielak-Orlicz-Sobolev spaces;
weak solutions; capacity solutions.
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Francisco Ortegón Gallego Departamento de Matemáticas Facultad de Ciencias, Universidad de Cádiz Campus del Río San Pedro 11510 Puerto Real, Cádiz, Spain email: francisco.ortegon@uca.es |
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Mohamed Rhoudaf Faculté des Sciences de Meknès Université Moulay-Ismaïl - Meknès Équipe: EDPs et Calcul Scientifique, Marocco email: rhoudafmohamed@gmail.com |
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Hajar Sabiki Laboratoire d'Analyse Géométrie et Applications Faculté des Sciences BP 133 Kénitra 14000, Marocco email: sabikihajar@gmail.com |
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