Potential nonclassical symmetries and solutions of fast diffusion equation

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 362, Issue 2-3, 2007, Pages 166-173

  Popovych, Roman O ^a,b   Vaneeva, Olena O ^a   Ivanova, Nataliya M ^a,c  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

^b UNIVERSITY OF VIENNA   (Austria)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

PARTIAL DIFFERENTIAL EQUATIONS;

FAST DIFFUSION EQUATIONS; POTENTIAL EQUATION; TRANSFORMATION GROUP;

DIFFUSION;

EID: 33846194257     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2006.10.015     Document Type: Article

References (32)

1. Ovsiannikov L.V. Dokl. Akad. Nauk SSSR 125 3 (1959) 492 (in Russian)
2. Amerov T.K. On conditional invariance of nonlinear heat equation. Theoretical and Algebraic Analysis of Equations of Mathematical Physics (1990), Institute of Mathematics, Kiev 12-14
3. Fushchych W.I., Serov M.I., and Amerov T.K. Proc. Acad. Sci. Ukraine 1 (1992) 26
4. Fushchych W.I., Serov N.I., and Tulupova L.A. Proc. Acad. Sci. Ukraine 4 (1993) 37
5. Gandarias M.L. Phys. Lett. A 286 (2001) 153
6. In: Ibragimov N.H. (Ed). Lie Group Analysis of Differential Equations-Symmetries, Exact Solutions and Conservation Laws vols. 1-3 (1994-1996), Chemical Rubber Company, Boca Raton, FL
7. Rosenau P. Phys. Rev. Lett. 74 7 (1995) 1056
8. Bakas I. C. R. Phys. 6 (2005) 175
9. Berryman J.G., and Holland C.J. J. Math. Phys. 23 (1982) 983
10. Bluman G.W., and Kumei S. Symmetries and Differential Equations (1989), Springer-Verlag, New York
11. Bluman G.W., Reid G.J., and Kumei S. J. Math. Phys. 29 (1988) 806
12. Bluman G.W., and Yan Z. Eur. J. Appl. Math. 16 (2005) 239
13. Akhatov I.Sh., Gazizov R.K., and Ibragimov N.Kh. Dokl. Akad. Nauk SSSR 293 (1987) 1033 (in Russian)
14. Akhatov I.Sh., Gazizov R.K., and Ibragimov N.Kh. Nonlocal symmetries. A heuristic approach. Itogi Nauki i Tekhniki, Current Problems in Mathematics, Newest Results vol. 34 (1989), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow 3-83, 195 (in Russian), Translated in
15. Akhatov I.Sh., Gazizov R.K., and Ibragimov N.Kh. Nonlocal symmetries. A heuristic approach. J. Sov. Math. 55 1 (1991) 1401
16. Polyanin A.D., and Zaitsev V.F. Handbook of Nonlinear Partial Differential Equations (2004), Chapman & Hall/CRC, Boca Raton, FL
17. Qu C. IMA J. Appl. Math. 62 (1999) 283
18. Fushchych W.I., Shtelen W.M., Serov M.I., and Popovych R.O. Proc. Acad. Sci. Ukraine 12 (1992) 28
19. Zhdanov R.Z., and Lahno V.I. Physica D 122 (1998) 178
20. Popovych R.O. On a class of Q-conditional symmetries and solutions of evolution equations. Symmetry and Analytic Methods in Mathematical Physics. Proceedings of Institute of Mathematics vol. 19 (1998), Institute of Mathematics, Kyiv 194-199 (in Ukrainian)
21. Popovych R.O., and Ivanova N.M. J. Phys. A 38 (2005) 3145. math-ph/0402066
22. Bluman G.W., and Cole J.D. J. Math. Mech. 18 11 (1969) 1025
23. Fushchych W.I., and Tsyfra I.M. J. Phys. A: Math. Gen. 20 (1987) L45
24. Zhdanov R.Z., Tsyfra I.M., and Popovych R.O. J. Math. Anal. Appl. 238 1 (1999) 101. math-ph/0207023
25. Olver P. Applications of Lie Groups to Differential Equations (1986), Springer-Verlag, New York
26. Ovsiannikov L.V. Group Analysis of Differential Equations (1982), Academic Press, New York
27. Fushchych W.I., and Zhdanov R.Z. Ukrainian Math. J. 44 7 (1992) 970
28. Popovych R.O., and Korneva I.P. On the Q-conditional symmetry of the linear n-dimensional heat equation. Symmetry and Analytic Methods in Mathematical Physics. Proceedings of Institute of Mathematics vol. 19 (1998), Institute of Mathematics, Kyiv 200-211 (in Ukrainian)
29. Popovych R.O. Equivalence of Q-conditional symmetries under group of local transformation. Proceedings of the Third International Conference "Symmetry in Nonlinear Mathematical Physics". Proceedings of Institute of Mathematics vol. 30 (2000), Institute of Mathematics, Kyiv 184-189. part 1 math-ph/0208005
30. R.O. Popovych, H. Eshraghi, Admissible point transformations of nonlinear Schrödinger equations, in: Proceedings of 10th International Conference in Modern Group Analysis (MOGRAN X), Larnaca, Cyprus, 2004, 2005, pp. 168-176
31. Kingston J.G., and Sophocleous C. J. Phys. A: Math. Gen. 31 (1998) 1597
32. Pukhnachov V.V. Nonlocal symmetries in nonlinear heat equations. Energy Methods in Continuum Mechanics. Oviedo, 1994 (1996), Kluwer Academic, Dordrecht 75-99