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Journal of Engineering Mathematics
Erschienen in: Journal of Engineering Mathematics 1/2015

01.04.2015

Lie symmetries of generalized Burgers equations: application to boundary-value problems

verfasst von: O. O. Vaneeva, C. Sophocleous, P. G. L. Leach

Erschienen in: Journal of Engineering Mathematics | Ausgabe 1/2015

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Abstract

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.
Vorheriger Artikel Macroscopic models for a mushy region in concrete corrosion
Nächster Artikel Bridging game theory and the knapsack problem: a theoretical formulation

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Fußnoten
1
Note that if \(a=1/n\), the equivalence group \(\hat{G}^\sim _2\) was found previously in [36] (see also [37, 38]) in the course of studying form-preserving (admissible) transformations of the class of generalized Burgers equations, \(u_t+uu_x+f(t,x)u_{xx}=0.\)
 
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Metadaten
Titel
Lie symmetries of generalized Burgers equations: application to boundary-value problems
verfasst von
O. O. Vaneeva
C. Sophocleous
P. G. L. Leach
Publikationsdatum
01.04.2015
Verlag
Springer Netherlands
Erschienen in
Journal of Engineering Mathematics / Ausgabe 1/2015
Print ISSN: 0022-0833
Elektronische ISSN: 1573-2703
DOI
https://doi.org/10.1007/s10665-014-9741-2

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