On the similarity solutions of the inhomogeneous nonlinear diffusion equation via symmetry method

Journal of the Physical Society of Japan

Volumn 73, Issue 1, 2004, Pages 42-48

  Khater, A H ^a,b   Malfliet, W ^b   Callebaut, D K ^b   Abdul Aziz, S F ^a  

^a Beni Suef University   (Egypt)

^b UNIVERSITY OF ANTWERP   (Belgium)

Author keywords

Calculus of variations and optimal control; Heat conduction; Nonlinear waves and nonlinear wave propagation; Partial differential equations; Waves and wave propagation: general mathematical aspects

Indexed keywords

EID: 24044452851     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.73.42     Document Type: Article

References (20)

1. A. H. Khater, W. Malfliet, M. H. M. Moussa and S. F. Abdul-Aziz: J. Phys. Soc. Jpn. 72 (2003) 2523.
2. E. A. Saied and M. M. Hussein: J. Phys. A 27 (1994) 4867.
3. E. A. Saied: J. Phys. Soc. Jpn. 64 (1995) 1092.
4. H. J. Pascal: J. Phys. A 25 (1992) 939.
5. G. W. Bluman and J. D. Cole: Similarity Methods for Differential Equations (Springer-Verlag, New York, 1974).
6. G. M. Murphy: Ordinary Differential Equations and their Solutions (Van Nostrand Reinhold, 1960).
7. O. P. Bhutani, G. Chandrasekaran and P. Mital: Int. J. Eng. Sci. 26 (1988) 243.
8. E. Tonti: Acad. R. Belg. Bull. Cl. Sci. 55 (1969) 137 (1st part);
9. E. Tonti: Acad. R. Belg. Bull. Cl. Sci. ibid. 55 (1969) 262 (2nd part).
10. H. Rund: Hamilton-Jacobi Theory in the Calculus of Variations (Princeton, New Jersey, 1966).
11. J. D. Logan: Invariant Variational Principles (Academic Press, New York, 1977).
12. E. L. Ince: Ordinary Differential Equations (Dover, New York, 1956).
13. J. R. King: J. Phys. A 23 (1990) 3681.
14. J. L. Lions: Quelques Méthodes de Résolution des Problémes aux Limites Nonlinéaires (Dunod, Gauthier-Villars, Paris, 1969) [in French].
15. A. Friedman: Applications of Nonlinear Partial Differential Equations in Mathematical Physics, ed. R. Finn (American Mathematical Society, Providence, RI, 1965) Proc. Symp. Applied Mathematics, Vol. 17, p. 3.
16. H. Fujita: J. Fac. Sci., Univ. Tokyo, Sect. IA 13 (1966) 109.
17. D. G. Aronson, M. G. Crandal and L. A. Peletier: Nonlinear Anal. 6 (1982) 1001.
18. V. A. Galaktinov, V. A. Dorodnitsyn, G. G. Elenin, S. P.Kurdyumov, and A. A. Samarskii: Itogi Tekniki, Ser. Sov. Probl. Mat. Nov. Dost. 28 (1986) 95
19. [Translation: J. Sov. Math. 41 (1988) 1222].
20. R. M. Miura: SIAM Rev. 18 (1976) 412.