RT journal article
T1 3D numerical simulation of an anisotropic bead type thermistor and multiplicity of solutions
A1 Lahrache, Manar
A1 Ortegón Gallego, Francisco
A1 Rhoudaf, Mohamed
A2 Matemáticas
K1 Thermistor problem
K1 Anisotropic Sobolev space
K1 Non-uniformly elliptic system
K1 Finite element method
K1 Numerical solution
AB We perform some 3D numerical experiments for the approximation of the solutions to a beadtype thermistor problem. We consider the case of a diagonal anisotropic diffusion matrix whose𝑗�th entry is of the form|𝜕�𝑢�∕𝜕�𝑥�𝑗�|𝑝�𝑗�−2𝜕�𝑢�∕𝜕�𝑥�𝑗�,𝑢� being the temperature inside the thermistor andthe exponents 𝑝�𝑗�,1 ≤ 𝑗� ≤ 3, lie in the interval (1,+∞). We first show some existence results fordifferent notions of solutions, prove a maximum principle for each type of solution, and studycertain symmetry properties for these solutions in a bead type thermistor. These properties leadus to the introduction of a symmetric solution and we show the existence of such a solution.We have developed a numerical algorithm for the computation of the numerical solutionsin a bead type thermistor. This algorithm combines a fixed-point technique with a standardfinite element method (FEM). Some numerical tests have shown the existence of non-symmetricsolutions and this leads to multiple many solutions (at least three). We discuss the numericalresults obtained for different values of the exponents 𝑝�𝑗� and the applied voltage on differentmeshes.
PB Elservier
SN 0378-4754
YR 2024
FD 2024-02-22
LK http://hdl.handle.net/10498/32742
UL http://hdl.handle.net/10498/32742
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026