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  4. Numerical simulation by Deep Learning of a time periodic p(x)-Laplace equation

Numerical simulation by Deep Learning of a time periodic p(x)-Laplace equation

MMC.
2024;
Volume 11, Number 2
: pp. 571–582
https://doi.org/10.23939/mmc2024.02.571
Received: April 03, 2024
Revised: June 19, 2024
Accepted: June 20, 2024

Alaa H., Ait Hsain T., Bentbib A. H., Aqel F., Alaa N. E.  Numerical simulation by Deep Learning of a time periodic $p(x)$-Laplace equation.  Mathematical Modeling and Computing. Vol. 11, No. 2, pp. 571–582 (2024)

Authors:
  1. H. Alaa
  2. T. Ait Hsain
  3. A. H. Bentbib
  4. F. Aqel
  5. N. E. Alaa
1
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University
2
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University
3
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University
4
Computer, Networks, Mobility and Modeling laboratory (IR2M), Faculty of Sciences and Technics, Hassan First University
5
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University

The objective of this paper is to focus on the study of a periodic temporal parabolic equation involving a variable exponent $p(x)$.  After proving the existence and uniqueness of the solution, we provide a method for its numerical simulation using emerging deep learning technologies.

periodic solution
p(x)-Laplace operator
deep learning
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