publication . Preprint . 2009

Projective analysis and preliminary group classification of the nonlinear fin equation $u_t=(E(u)u_x)_x + h(x)u$

Nadjafikhah, Mehdi; Mahdipour-Shirayeh, Ali;
Open Access English
  • Published: 26 Aug 2009
In this paper we investigate for further symmetry properties of the nonlinear fin equations of the general form $u_t=(E(u)u_x)_x + h(x)u$ rather than recent works on these equations. At first, we study the projective (fiber-preserving) symmetry to show that equations of the above class can not be reduced to linear equations. Then we determine an equivalence classification which admits an extension by one dimension of the principal Lie algebra of the equation. The invariant solutions of equivalence transformations and classification of nonlinear fin equations among with additional operators are also given.
free text keywords: Mathematics - Differential Geometry, 34C14, 35J05, 70G65
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19 references, page 1 of 2

[1] P. Basarab-Horwath, V. Lahno and R. Zhdanov, The structure of Lie algebras and the classification problem for partial differential equation, Acta Appl. Math. 69 ( 2001) 4394.

[2] Bokhari A.H., Kara A.H. and Zaman F.D., A note on a symmetry analysis and exact solutions of a nonlinear fin equation, Appl. Math. Lett. 19 (2006) 13561340. [OpenAIRE]

[3] V.A. Dorodnitsyn, On invariant solutions of non-linear heat equation with a source, Zh. Vychisl. Mat. Mat. Fiz. 22 (1982) 13931400 (in Russian).

[4] F. Klein, Ges. math. Abhandl., Bd. 1, Berlin, S. 585, 1921.

[5] S. Lie, Begru¨ndung einer Invariantenthoerie der Beru¨hrungstransformationen, Math. Ann. 8 Heft 2 (1874) 215-288.

[6] L. Song and H. Zhang, Preliminary group classification for the nonlinear wave equation utt = f (x, u)uxx + g(x, u), Nonlinear Analysis (2008), doi:10.1016/

[7] I. Kola´r, P.W. Michor and J. Slovak, Natural Operations in Differential Geometry, Springer-Verlag, Berlin Heidelberg, 1993.

[8] N.H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differentail Equations, John Wiley & Sons, England, 1999.

[9] N.H. Ibragimov, Lie group analysis of differential equations - symmetries, exact solutions and conservation laws, Vol. 1, Boca Raton, FL, Chemical Rubber Company, 1994.

[10] N.H. Ibragimov, Selected works, Vol. II, ALGA Publications, Blekinge Institute of Technology Karlskrona, Sweden, 2006. [OpenAIRE]

[11] V.I. Lahno, S.V. Spichak and V.I. Stognii, Symmetry Analysis of Evolution Type Equations (Kyiv: Institute of Mathematics of NAS of Ukraine), 2002.

[12] N.H. Ibragimov, Transformation Groups Applied to Mathematical Physics, D. Reidel Publishing Company, Dordrecht, Holland, 1985.

[13] P.J. Olver, Equivalence, Invariants, and Symmetry, Cambridge Univ. Press, Cambridge, 1995.

[14] L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982.

[15] M. Pakdemirli and A.Z. Sahin, Similarity analysis of a nonlinear fin equation, Appl. Math. Lett. 19 (2006) 378384. [OpenAIRE]

19 references, page 1 of 2
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