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  4. Semilinear periodic equation with arbitrary nonlinear growth and data measure: mathematical analysis and numerical simulation

Semilinear periodic equation with arbitrary nonlinear growth and data measure: mathematical analysis and numerical simulation

MMC.
2023;
Volume 10, Number 3
: pp. 956–964
https://doi.org/10.23939/mmc2023.03.956
Received: June 12, 2022
Revised: August 16, 2023
Accepted: August 26, 2023

Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 956–964 (2023)

Authors:
  1. M. El Ghabi
  2. H. Alaa
  3. 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

In this work, we are interested in the existence, uniqueness, and numerical simulation of weak periodic solutions for some semilinear elliptic equations with data measures and with arbitrary growth of nonlinearities.  Since the data are not very regular and the growths are arbitrary, a new approach is needed to analyze these types of equations.  Finally, a suitable numerical discretization scheme is presented.  Several numerical examples are given which show the robustness of our algorithm.

periodic solution
semilinear equation
optimisation method
numerical simulation
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