A New Class of Symmetry Reductions for Parameter Identification Problems

DOI

10.1142/S1402925109000273How to use a DOI?

Keywords

Lie groups of transformations; classical symmetries; nonclassical symmetries; nonlinear partial differential equations; parameter identification problems

Abstract

This paper introduces a new type of symmetry reductions called extended nonclassical symmetries that can be studied for parameter identification problems described by partial differential equations. Including the data function in the parameter space, we show that specific data and parameter classes that lead to a reduced dimension model can be found. More exactly, since the extended nonclassical symmetries relate the forward and inverse problems, the dimension of the studied equation may be reduced by expressing the data and parameter in terms of the group invariants. The main advantage of these new symmetries is that they may be incorporated into the boundary conditions as well, and, consequently, the dimension reduction problem can be analyzed on new types of domains. Special group-invariant solutions or additional information on the parameter can be obtained. Besides, in the case of the first-order partial differential equations, this symmetry reduction method might be an effective alternative tool for finding particular analytical solutions to the studied model, especially when the Maple subroutine pdsolve does not output satisfactory results. As an example, we consider the nonlinear stationary heat conduction equation. Our MAPLE routine GENDEFNC which uses the package DESOLV (authors Carminati and Vu) has been updated for this propose and its output is the nonlinear partial differential equation system of the determining equations of the extended nonclassical symmetries.

Copyright

© 2009 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Nicoleta Bîlă
AU  - Jitse Niesen
PY  - 2021
DA  - 2021/01/07
TI  - A New Class of Symmetry Reductions for Parameter Identification Problems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 355
EP  - 371
VL  - 16
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000273
DO  - 10.1142/S1402925109000273
ID  - Bîlă2021
ER  -