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arXiv · 1303.3548

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

O. O. Vaneeva·C. Sophocleous·P. G. L. Leach
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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 nonlinear acoustics we show that that the "direct" procedure of solving boundary-value problems using Lie symmetries firstly described by Bluman is more general and straightforward than the method suggested by Moran and Gaggioli in [J. Eng. Math. 3 (1969), 151-162]. After the group classification of a class of generalized Burgers equations with time-dependent viscosity is performed we solve an associated boundary-value problem using the symmetries obtained.

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O. O. Vaneeva, C. Sophocleous, P. G. L. Leach. 2013-03-14. Lie symmetries of generalized Burgers equations: application to boundary-value problems. https://arxiv.org/abs/1303.3548

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