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Lie symmetry analysis of the Hopf functional-differential equation

Lie-Symmetrieanalyse der Hopf-Funktionaldifferentialgleichung

Masterarbeit 2015 33 Seiten

Ingenieurwissenschaften - Maschinenbau

Zusammenfassung

In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of OBERLACK and WACŁAWCZYK (2006, Arch. Mech., 58, 597), (2013, J. Math. Phys., 54, 072901) where the extended Lie symmetry analysis is performed in the Fourier space.

Here, we introduce a method to perform the extended Lie symmetry analysis in the physical space where we have to deal with the transformation of the integration variable in the appearing integral terms. The method is based on the transformation of the product y(x)dx appearing in the integral terms and applied to the functional formulation of the viscous Burgers equation.

The extended Lie symmetry analysis furnishes all known symmetries of the viscous Burgers equation and is able to provide new symmetries associated with the Hopf formulation of the viscous Burgers equation. Hence, it can be employed as an important tool for applications in continuum mechanics.

Details

Seiten
33
Jahr
2015
ISBN (Buch)
9783668058477
Dateigröße
783 KB
Sprache
Deutsch
Katalognummer
v307089
Institution / Hochschule
Technische Universität Darmstadt – Fachbereich Maschinenbau, Fachgebiet für Strömungsdynamik, AG Turbulence theory and modelling
Note
1,0
Schlagworte
Lie symmetries Hopf equation Burgers equation functional differential equations turbulence integro-differential equations Lie Symmetrieanalyse Hopf-Funktionaldifferentialgleichung

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Titel: Lie symmetry analysis of the Hopf functional-differential equation