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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

On the Variational Symmetries of P.D.E's Incorporating Boundary Value Constraints

Uchechukwu Michael Opara1,2, Festus Irimisose Arunaye2, Henrietta Ify Ojarikre2 and Philip Olugbenga Mate3
  • 1 Department of Pure and Applied Physics, Veritas University, Abuja, Nigeria
  • 2 Department of Mathematics, Delta State University (DELSU), Abraka, Delta State, Nigeria
  • 3 Department of Mathematics, Veritas University, Abuja, Nigeria

Abstract

A crucial interface between Optimization theory, Trace theory, and Lie Symmetry theory is brought to the fore in this paper, as an enhancement of standard known results established in Partial Differential Equation (P.D.E) analysis. In particular, the incorporation of compatible Boundary Value constraints in the re-assessment of admitted variational symmetries is a key process in the development of the discussions and results. Classical variational formulation techniques for a few Boundary Value Problems are considered. Ramifications of standard and modified admitted variational symmetries in simplification of PDEs constitute further relevant crucial details addressed appreciably.

Journal of Mathematics and Statistics
Volume 21 No. 1, 2025, 1-7

DOI: https://doi.org/10.3844/jmssp.2025.1.7

Submitted On: 2 June 2024 Published On: 22 January 2025

How to Cite: Opara, U. M., Arunaye, F. I., Ojarikre, H. I. & Mate, P. O. (2025). On the Variational Symmetries of P.D.E's Incorporating Boundary Value Constraints. Journal of Mathematics and Statistics, 21(1), 1-7. https://doi.org/10.3844/jmssp.2025.1.7

Open AccessCopyright: © 2025 Uchechukwu Michael Opara, Festus Irimisose Arunaye, Henrietta Ify Ojarikre and Philip Olugbenga Mate. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Boundary Value Problems
  • Calculus of Variations
  • Classical Lagrangians
  • Symmetry Invariant Solutions
  • Laplace's Equation
  • Poisson Equation