International Journal of Numerical Methods and Applications

The International Journal of Numerical Methods and Applications publishes research articles on numerical methods and their applications in various fields, including differential equations, fluid dynamics, and bioinformatics. It also welcomes survey articles on new methods in numerical analysis.

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OPTIMAL NECESSARY CONDITIONS OF COMMANDS FOR A NONLINEAR HYPERBOLIC PROBLEM WITH CONTINUOUS MEAN SQUARE POTENTIAL

Authors

  • Arno Chadel MANKESSI
  • Dieudonné AMPINI

Keywords:

optimal condition, nonlinear hyperbolic equation, commands

DOI:

https://doi.org/10.17654/0975045224011

Abstract

This paper is devoted to the study of the optimal necessary conditions of a nonlinear hyperbolic equation with homogeneous Neumann condition, the initial conditions examined in [1]. For this, we constructed an integral functional depending on the solution of the problem and the commands (second member and initial conditions of the equation) whose differentiability has been shown in [2]. Then, we minimize the integral functional with equality and inequality type constraints which allowed us to obtain the optimal conditions of the first order from a conjugate problem obtained in [2] of which we generate the Hamiltonian form.

Received: July 4, 2024
Accepted: July 23, 2024

References

Arno Chadel MANKESSI and Dieudonné AMPINI, Existence and uniqueness of the solution of a non linear hyperbolic problem with a continuous potential in mean square, Far East Journal of Applied Mathematics 116(2) (2023), 99-132.

Dieudonné AMPINI and Arno Chadel MANKESSI, Differentiability in the sens of Fréchet of a functional related to a nonlinear hyperbolic problem and depending on commands, Scientific Journal 13(2) (2024), 223-261.

https://doi.org/10.37418/amsj.13.2.5.

Dieudonné AMPINI, Necessary conditions of optimaly for non linear hyperbolic problem, Annales de l’Université de l’Amitié des peuples de Moscou Vestnik, Série Mathématiques 9(1) (2002), 29-55.

Sylvie Benzonie-GAVAGE, Calcul differentiel et équations differentielles, Dunod Paris, 2010.

Jacques CEA, Optimisation: théorie et algorithme, Dunod Paris, 1971.

Jean-Christophe CULIOLI, Introduction à l’optimisation, deuxième edition Ellipse, 2012.

Jean-Baptiste Hitiart-URRUTY, Optimisation et analyse convexe, Edp Sciences, 2009.

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Published

2024-08-09

Issue

Vol. 24 No. 2 (2024)

Section

Articles

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How to Cite

OPTIMAL NECESSARY CONDITIONS OF COMMANDS FOR A NONLINEAR HYPERBOLIC PROBLEM WITH CONTINUOUS MEAN SQUARE POTENTIAL. (2024). International Journal of Numerical Methods and Applications, 24(2), 165-179. https://doi.org/10.17654/0975045224011

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