Lie symmetry analysis of the Hopf functional-differential equation

Masterarbeit aus dem Jahr 2015 im Fachbereich Ingenieurwissenschaften - Maschinenbau Note: 10 Technische Universität Darmstadt (Fachbereich Maschinenbau Fachgebiet für Strömungsdynamik AG Turbulence theory and modelling) Sprache: Deutsch Abstract: 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 WACLAWCZYK (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.