3D numerical simulation of an anisotropic bead type thermistor and multiplicity of solutions

Manar Lahrache, Francisco Ortegón Gallego and Mohamed Rhoudaf

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 220, issue C, 640-672

Abstract: We perform some 3D numerical experiments for the approximation of the solutions to a bead type thermistor problem. We consider the case of a diagonal anisotropic diffusion matrix whose jth entry is of the form |∂u/∂xj|pj−2∂u/∂xj, u being the temperature inside the thermistor and the exponents pj, 1≤j≤3, lie in the interval (1,+∞). We first show some existence results for different notions of solutions, prove a maximum principle for each type of solution, and study certain symmetry properties for these solutions in a bead type thermistor. These properties lead us to the introduction of a symmetric solution and we show the existence of such a solution.

Keywords: Thermistor problem; Anisotropic Sobolev space; Non-uniformly elliptic system; Finite element method; Numerical solution (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:220:y:2024:i:c:p:640-672

DOI: 10.1016/j.matcom.2024.02.018

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