Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 84, pp. 1-32.

Title: Existence of a solution and its numerical approximation for a strongly nonlinear
coupled system in anisotropic Orlicz-Sobolev spaces
       
Authors: Francisco Ortegon Gallego (Univ. de Cadiz, Spain)
         Hakima Ouyahya  (Moulay Ismail Univ., Meknes, Morocco)
         Mohamed Rhoudaf (Moulay Ismail Univ., Meknes, Morocco)
         
Abstract:
We study the existence of a capacity solution for a nonlinear elliptic
coupled system in anisotropic Orlicz-Sobolev spaces.
The unknowns are the temperature inside a semiconductor material,
and the electric potential.
This system may be considered as a generalization of the steady-state
thermistor problem. The numerical solution is also analyzed by means of the
least squares method in combination with a conjugate gradient technique.

Submitted April 21, 2022. Published December 21, 2022.
Math Subject Classifications: 35J70, 35J66, 46E30, 65N22.
Key Words: Nonlinear elliptic equations; capacity solution; least squares method;
          anisotropic Orlicz-Sobolev spaces; conjugate gradient algorithm.