On the porous medium equation with modified Fourier's law: Symmetries and integrability

Journal of the Physical Society of Japan

Volumn 68, Issue 2, 1999, Pages 360-368

  Saied, Effat A ^a   Abd El Rahman, Reda G ^a  

^a BENHA UNIVERSITY   (Egypt)

Author keywords

Fourier's law and symmetry method; The porous medium equation

Indexed keywords

EID: 0042285249     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.68.360     Document Type: Article

References (34)

1. S. Kamin and P. Rosenau: Communs Pure Appl. Math. 34 (1981) 831.
2. S. Kamin and P. Rosenau: Communs Pure Appl. Math. 35 (1982) 113.
3. S. Antiochos and P. Sturrock: Sol. Phys. 49 (1976) 359.
4. G. Barenblatt: Prikl. Mat. Mekh. 16 (1952) 67.
5. J. Crank: The Mathematics of Diffusion (Oxford University Press, 1975) 2nd ed., Chap. 13.
6. H. Conway and H. Lee: J. Lubr. Technol. 99 (1977) 376.
7. J. Buckmaster: J. Fluid Mech. 81 (1977) 735.
8. A. Lacey, J. Ockendon and D. Turcotte: Earth Planet Sci. Lett. 54 (1981) 139.
9. A. Lacey, J. Ockendon and A. Tayler: SIAM J. Appl. Math. 42 (1982) 1252.
10. D. Aronson and J. Gravelau: Euro. J. Appl. Math. 4 (1993) 65.
11. J. R. King: J. Phys. A: Math. Gen. 25 (1992) 4861.
12. J. R. King: J. Phys. A: Math. Gen. 23 (1990) 3681 & 5441.
13. J. Hill: Differential Equations and Group Methods (FL, Chemical Rubber, Boca Raton, 1992).
14. J. Hill: J. Eng. Math. 23 (1989) 141.
15. E. A. Saied and M. H. Magdy: J. Phys. A: Math. Gen. 27 (1994) 4867.
16. E. A. Saied: J. Phys. Soc. Jpn. 64 (1995) 1092.
17. E. A. Saied: J. Phys. Soc. Jpn. 67 (1998) 101.
18. E. A. Saied and M. H. Magdy: J. Nonlinear Math. Phys. 3 (1996) 219, No. 1/2.
19. M. P. Edwards: Phys. Lett. A 190 (1994) 149.
20. A. Oron and P. Rosenau: Phys. Lett. A 118 (1986) 172.
21. J. R. Philip: J. Aust. Math. Soc., Ser. B 33 (1992) 363.
22. D. Joseph and L. Preziosi: Heat Waves Rev. Mod. Phys. 61 (1989) 41.
23. W. Israel: Covariant Fluid Mechanics and Thermodynamics: An Introduction Lecture Notes in Mathematics 1385 (Springer, Berlin, 1987).
24. Ya. Zeldovich and Yu. Raizer: Physics of Shock Waves and High-temperature Hydrodynamic Phenomena (Academic, New York, 1967) Vol. II.
25. H. Pascal: J. Phys. A: Math. Gen. 25 (1992) 939.
26. A. Fokas and Y. Yortos: SIAM J. Appl. Math. 42 (1982) 318.
27. M. Edwards and P. Broadbridge: J. Phys. A: Math. Gen. 28 (1995) 5455.
28. G. Rosen: Phys. Rev. Lett. 49 (1982) 1844.
29. D. Smiles and M. Rosenthal: Aust. J. Soil. Res. 6 (1968) 237.
30. P. Olver: Applications of Lie Group to Differential Equations (Springer, Berlin, 1986).
31. G. W. Bluman: Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics (Kluwer, Dordrecht, 1993).
32. L. V. Ovsiannikov: Group Analysis of Differential Equations (Academic, New York, 1982).
33. N. H. Ibragimov: Handbook of Lie Group Analysis of Differential Equations (Fl, Chemical Rubber, Boca Raton, 1994).
34. E. L. Ince: Ordinary Differential Equations (Dover. New-York, 1956).