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On double reductions from symmetries and conservation laws. (English) Zbl 1179.35038
Summary: We present the theory of double reductions of PDEs with two independent variables that admit a Lie point symmetry and a conserved vector invariant under the symmetry. The theory is applied to a third order nonlinear partial differential equation which describes the filtration of a visco-elastic liquid with relaxation through a porous medium.

MSC:
35B06 Symmetries, invariants, etc. in context of PDEs
76S05 Flows in porous media; filtration; seepage
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[1] Kara, A.; Mahomed, F., The relationship between symmetries and conservation laws, Int. J. theor. phys., 39, 1, 23-40, (2000) · Zbl 0962.35009
[2] Kara, A.; Mahomed, F., A basis of conservation laws for partial differential equations, J. nonlinear math. phys, 9, Suppl. 2, 60-72, (2002) · Zbl 1362.35024
[3] Sjöberg, A., Double reduction of PDEs from the association of symmetries with conservation laws with applications, Appl. math. comput., 184, 608-616, (2007) · Zbl 1116.35004
[4] Euler, N.; Steeb, W.-H., Continuous symmetries, Lie algebras and differential equations, (1992), B.I. Wissenschaftsverlag Mannheim, Leipzig, Wien, Zürich · Zbl 0764.35098
[5] Steeb, W.-H., Continuous symmetries, Lie algebras, differential equations and computer algebra, (1996), World Scientific Publishing Co. Pty. Ltd. Singapore · Zbl 0916.34001
[6] Olver, P., ()
[7] Stephani, H., Differential equations: their solutions using symmetries, (1989), Cambridge University Press Cambridge
[8] Bluman, G.; Kumei, S., ()
[9] V. Baikov, Filtration of a non-Newtonian liquid in porous media: Models, symmetries and solutions, in: Interdisciplinary Workshop on Symmetry Analysis and Mathematical Modelling, University of the North-West, Mmabatho, 1988
[10] Ö. Kartal, Visco-elastic liquid with relaxation: Symmetries, conservation laws and solutions, Dissertation, University of Johannesburg, Auckland Park Campus, Gauteng, 2004
[11] Sjöberg, A.; Kartal, Ö., Filtration of a visco-elastic liquid with relaxation: A note on Lie point symmetries and reductions, J. nonlinear math. phys., 15, Suppl. 1, 203-210, (2008) · Zbl 1362.35008
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