Further transformation properties of generalised inhomogeneous nonlinear diffusion equations with variable coefficients

Physica A: Statistical Mechanics and its Applications

Volumn 345, Issue 3-4, 2005, Pages 457-471

  Sophocleous, Christodoulos ^a  

^a UNIVERSITY OF CYPRUS   (Cyprus)

Author keywords

Form preserving transformations; Hodograph transformations; Local and nonlocal symmetries; Nonlinear diffusion equations

Indexed keywords

HEAT CONDUCTION; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MOLECULAR DYNAMICS; NONLINEAR EQUATIONS; PLASMA THEORY;

FORM-PRESERVING TRANSFORMATIONS; HODOGRAPH TRANSFORMATIONS; LOCAL AND NONLOCAL SYMMETRIES; NONLINEAR DIFFUSION EQUATIONS;

DIFFUSION;

EID: 9644307867     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(04)01004-0     Document Type: Article

References (24)

1. W.F. Ames, Nonlinear Partial Differential Equations in Engineering, vol. I, II, Academic Press, New York, 1972.
2. L.A. Peletier, Applications of Nonlinear Analysis in the Physical Sciences, Pitman, London, 1981.
3. J. Crank, The Mathematics of Diffusion, second ed., Oxford, London, 1979.
4. J.G. Berryman, J.G. Holland, Nonlinear diffusion problems arising in plasma physics, Phys. Rev. Lett. 40 (1978) 1720-1722.
5. Y.S. Touloukian, P.W. Powell, C.Y. Ho, P.O. Klemens, Thermodynamics Properties of Matter, vol. 1, Plenum Press, New York, 1970.
6. A. Munier, J.R. Burgan, J. Gutierrez, E. Fijalkow, M.R. Feix, Group transformations and the nonlinear heat diffusion equation, SIAM J. Appl. Math. 40 (1981) 191-207.
7. S. Kamin, P. Rosenau, Propagation of thermal waves in an inhomogeneous medium, Comm. Pure Appl. Math. 34 (1981) 831-852.
8. J.M. Hill, Similarity solutions for nonlinear diffusion-a new integration procedure, J. Eng. Math. 23 (1989) 141-155.
9. D.L. Hill, J.M. Hill, Similarity solutions for nonlinear diffusion-further exact solutions, J. Eng. Math. 24 (1990) 109-124.
10. J.R. King, Exact similarity solutions to some nonlinear diffusion equations, J. Phys. A 23 (1990) 3681-3697.
11. J.R. King, Exact solutions to a nonlinear diffusion equation, J. Phys. A 24 (1991) 3213-3216.
12. C. Sophocleous, Classification of potential symmetries of generalised inhomogeneous nonlinear diffusion equations, Physica A 320 (2003) 169-183.
13. N.H. Ibragimov, Lie Group Analysis of Differential Equations - Symmetries Exact Solutions and Conservation Laws, vol. 1, Chemical Rubber Company, Boca Raton, FL, 1994.
14. C. Sophocleous, Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations, Physica A 324 (2003) 509-529.
15. J.G. Kingston, C. Sophocleous, On form-preserving point transformations of partial differential equations, J. Phys. A: Math. Gen. 31 (1998) 1597-1619.
16. C. Sophocleous, Hodograph-type transformations, Nonlinear Anal. 55 (2003) 441-466.
17. P.A. Clarkson, A.S. Fokas, M.J. Ablowitz, Hodograph transformations for linearizable partial differential equations, SIAM J. Appl. Math. 49 (1989) 1188-1209.
18. N. Euler, M. Euler, A tree of linearisable second-order evolution by generalised hodograph transformations, J. Nonlinear Math. Phys. 8 (2001) 342-362.
19. G.W. Bluman, S. Kumei, Symmetries and Differential Equations, Springer, New York, 1989.
20. G.W. Bluman, G.J. Reid, S. Kumei, New classes of symmetries for partial differential equations, J. Math. Phys. 29 (1988) 806-811.
21. G.W. Bluman, Potential symmetries and equivalent conservation laws, in: N.H. Ibragimov, M. Torrisi, A. Valenti (Eds.), Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics (Acireale, 1992), Kluwer Academic Publications, Dordrecht, 1993, pp. 71-84.
22. P.J. Olver, Application of Lie Groups to Differential Equations, Springer, New York, 1986.
23. N.H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, Wiley, New York, 1999.
24. N. Euler, M.L. Gandarias, M. Euler, O. Lindblom, Auto-hodograph transformations for a hierarchy of nonlinear evolution equations, J. Math. Anal. Appl. 257 (2001) 21-28.