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

: pp. 571–582
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)

Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University
Computer, Networks, Mobility and Modeling laboratory (IR2M), Faculty of Sciences and Technics, Hassan First University
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.

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