Equivalence group of a fourth-order evolution equation unifying various non-linear models

Communications in Nonlinear Science and Numerical Simulation

Volumn 13, Issue 2, 2008, Pages 259-268

  Gandarias, Maria Luz ^a   Ibragimov, Nail H ^b  

^a UNIVERSITY OF CÁDIZ   (Spain)

^b BLEKINGE INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Equivalence transformations; Non linear models; Theorem on projections; Thin liquid films

Indexed keywords

MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; PARTIAL DIFFERENTIAL EQUATIONS; THIN FILMS;

EQUIVALENCE TRANSFORMATIONS; NON-LINEAR MODELS; THEOREM ON PROJECTIONS; THIN LIQUID FILMS;

LIQUID FILMS;

LIQUID FILMS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; PARTIAL DIFFERENTIAL EQUATIONS; THIN FILMS;

EID: 34548149779     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2005.12.011     Document Type: Article

References (16)

1. Qu C. Symmetries and solutions to the thin film equations. J Math Anal Appl 2006;317(2), in press.
2. Bernoff A.J., and Bertozzi A.L. Singularities in a modified Kuramoto-Sivashinsky equation describing interface motion for phase transition. Physica D 85 (1995) 375-404
3. Hocherman T., and Rosenau P. On KS-type equations describing the evolution and rupture of a liquid interface. Physica D 67 (1993) 113-125
4. Bertozzi A.L., and Pugh M. Long-wave instabilities and saturation in thin film equations. Comm Pur Appl Math LI (1998) 625-651
5. Greenspan H.P. J Fluid Mech 84 (1978) 125-143
6. Bertozzi A.L. SIAM J Appl Math 56 (1996) 681-714
7. Smyth N.F., and Hill J.M. IMA J Appl Math 40 (1988) 73-86
8. Gandarias ML, Medina E. In: Proceedings NEEDS 1999.
9. Gandarias M.L., and Medina E. Europhys Lett 55 (2001) 143-149
10. Ehrhard P. J Colloids Interface Sci 168 (1994) 242-246
11. Williams M.B., and Davis S.H. J Colloids Interface Sci 90 (1982) 220-228
12. In: Ibragimov N.H. (Ed). CRC handbook of Lie group analysis of differential equations. Symmetries, exact solutions and conservation laws vol. 1 (1994), CRC Press Inc., Boca Roton
13. Akhatov I.Sh., Gazizov R.K., and Ibragimov N.H. Nonlocal symmetries: heuristic approach. Itogi Nauki i Tekhniki. Sovremennie problemy matematiki: Noveishye dostizhenia 34 (1989) 3-84 [English transl in J Sov Math 1991;55(1):1401-50]
14. x). J Math Phys 32 11 (1991) 2988-2995
15. Ovsyannikov L.V. Group analysis of differential equations (1978), Nauka, Moscow [English transl. Ames WF, editor. Academic Press, 1982]
16. Ibragimov NH. Theorem on projections of equivalence Lie algebras. 1987, unpublished.