caa a22 4500 606166971 CHVBK 20210128100700.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10665-014-9741-2 doi (NATIONALLICENCE)springer-10.1007/s10665-014-9741-2 Lie symmetries of generalized Burgers equations: application to boundary-value problems [Elektronische Daten] [O. Vaneeva, C. Sophocleous, P. Leach] 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. Springer Science+Business Media Dordrecht, 2014 Boundary-value problems nationallicence Burgers equation nationallicence Group classification nationallicence Lie symmetries nationallicence Vaneeva O. Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivska Str., 01601, Kiev-4, Ukraine aut Sophocleous C. Department of Mathematics and Statistics, University of Cyprus, 1678, Nicosia, Cyprus aut Leach P. Department of Mathematics and Statistics, University of Cyprus, 1678, Nicosia, Cyprus aut Journal of Engineering Mathematics Springer Netherlands 91/1(2015-04-01), 165-176 0022-0833 91:1<165 2015 91 10665 https://doi.org/10.1007/s10665-014-9741-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-014-9741-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Vaneeva O. Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivska Str., 01601, Kiev-4, Ukraine aut NATIONALLICENCE 700 1- Sophocleous C. Department of Mathematics and Statistics, University of Cyprus, 1678, Nicosia, Cyprus aut NATIONALLICENCE 700 1- Leach P. Department of Mathematics and Statistics, University of Cyprus, 1678, Nicosia, Cyprus aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 91/1(2015-04-01), 165-176 0022-0833 91:1<165 2015 91 10665