Lie symmetries of generalized Burgers equations: application to boundary-value problems
Date
2015Source
Journal of Engineering MathematicsVolume
91Issue
1Pages
165-176Google Scholar check
Keyword(s):
Metadata
Show full item recordAbstract
There exist several approaches exploiting Lie symmetries in the reduction of boundary-value problems for partial differential equations modelling real-world phenomena to those problems for ordinary differential equations. Using an example of generalized Burgers equations appearing in non-linear acoustics we show that the direct procedure of solving boundary-value problems using Lie symmetries first described by Bluman is more general and straightforward than the method suggested by Moran and Gaggioli [J Eng Math 3:151–162, 1969]. After performing group classification of a class of generalized Burgers equations with time-dependent viscosity we solve an associated boundary-value problem using the symmetries obtained. © 2014, Springer Science+Business Media Dordrecht.
Collections
Cite as
Related items
Showing items related by title, author, creator and subject.
-
Article
Conservation laws and hierarchies of potential symmetries for certain diffusion equations
Ivanova, Nataliya M.; Popovych, R. O.; Sophocleous, Christodoulos; Vaneeva, Olena O. (2009)We show that the so-called hidden potential symmetries considered in a recent paper [M.L. Gandarias, New potential symmetries for some evolution equations, Physica A 387 (2008) 2234-2242] are ordinary potential symmetries ...
-
Article
Kansa-RBF algorithms for elliptic problems in axisymmetric domains
Karageorghis, Andreas; Chen, C. S.; Liu, X. -Y (2016)We employ a Kansa-radial basis function method for the numerical solution of elliptic boundary value problems in three-dimensional axisymmetric domains. We consider problems governed by the Poisson equation, the inhomogeneous ...
-
Article
A Kansa-Radial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains
Liu, X. -Y; Karageorghis, Andreas; Chen, C. S. (2015)We employ a Kansa-radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains. This discretization leads, with an appropriate selection of collocation points and for ...