Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 83
The existence and uniqueness of a weak solution for a thermistor problem
Ibrahim Dahi, Moulay Rchid Sidi Ammi
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 04, 2022
March 03, 2079
April 15, 2079

Abstract: In this work, we study a much more general version of a thermistor problem than the one considered by Xu in [1]; Precisely, we assume that the diffusion function a(x, t, u, ∇u) depends also on u and define a Leray–Lions operator of order p ≥ 2. Since capacity solutions are obtained by approximating techniques, the proof of the existence theorem relies on the introduction of a sequence of approximate problems. Then, it is shown that the sequence of solutions to these smooth problems converge (up to a subsequence) in a certain sense to a capacity solution. As a consequence, we get the ...