Anomalous diffusion with absorption: Exact time-dependent solutions

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 2, 2000, Pages 1417-1422

  Drazer, German ^a   Wio, Horacio S ^b   Tsallis, Constantino ^c,d  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b INSTITUTO BALSEIRO   (Argentina)

^c UNIVERSITY OF NORTH TEXAS   (United States)

^d CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

FOKKER PLANCK EQUATION; NONLINEAR EQUATIONS;

ABSORPTION PROCESS; ANOMALOUS DIFFUSION; NONLINEAR DIFFUSION; NONLINEAR FOKKER-PLANCK EQUATIONS; TIME-DEPENDENT SOLUTIONS;

DIFFUSION;

EID: 0000572748     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.1417     Document Type: Article

References (42)

1. H. Spohn, J. Phys. I 3, 69 (1993).
2. O.V. Bychuk and B. O’shugness, Phys. Rev. Lett. 74, 1795 (1995).
3. T. Solomon, E. Weeks, and H. Swinney, Phys. Rev. Lett. 71, 3975 (1993).
4. J.D. Murray, Mathematical Biology (Springer-Verlag, Berlin, 1989).
5. M. Doi and S.F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986).
6. Y. Fukai, The Metal-Hydrogen System (Springer-Verlag, Berlin, 1993).
7. D.E. Strier, D.H. Zanette, and H.S. Wio, Physica A 226, 310 (1996).
8. A.R. Plastino and A.L. Plastino, Physica A 222, 347 (1995).
9. A. Compte and D. Jou, J. Phys. A 29, 4321 (1996).
10. C. Tsallis and D.J. Bukman, Phys. Rev. E 54, R2197 (1996).
11. C. Tsallis, J. Stat. Phys. 52, 479 (1988)
12. E.M.F. Curado and C. Tsallis, J. Phys. A 24, L69 (1991)
13. J. Phys. AE.M.F. CuradoC. Tsallis24, 3187 (1991)
14. J. Phys. AE.M.F. CuradoC. Tsallis25, 1019 (1992)
15. A.R. Plastino and A. Plastino, Phys. Lett. A 174, 384 (1993)
16. D.H. Zanette and P.A. Alemany, Phys. Rev. Lett. 75, 366 (1995)
17. B.M. Boghosian, Phys. Rev. E 53, 4754 (1996)
18. V.H. Hamity and D.E. Barraco, Phys. Rev. Lett. 76, 4664 (1996)
19. Phys. Rev. Lett.A.K. Rajagopal, 76, 3469 (1996)
20. C. Tsallis and A.M.C. de Souza, Phys. Lett. A 235, 444 (1997).A regularly updated bibliography on the subject is accessible at http://tsallis.cat.cbpf.br/biblio.htm.A set of mini-reviews is available at http://sbf.if.usp.br/WWW(Formula presented)pages/Journals/BJP/Vol29/ Num1/index.htm.
21. M. Muskat, The Flow of Homogeneous Fluids Through Porous Media (McGraw-Hill, Michigan, 1937).
22. Flow Through Porous Media, edited by J.M. De Wiest (Academic Press, New York, 1969).
23. J. Crank, The Mathematics of Diffusion (Oxford University Press, London, 1956).
24. G. Drazer, R. Chertcoff, L. Bruno, and M. Rosen (unpublished).
25. P.Y. Polubarinova-Kochina, Theory of Ground Water Movement (Princeton University Press, 1962)
26. L.A. Peletier, Applications of Nonlinear Analysis in the Physical Sciences (Pitman Adv. Pub. Prog., Boston, 1981), Chap. 11.
27. D. Massignon, in Uranium Enrichment, edited by S. Villani, Topics in Applied Physics Vol. 35 (Springer-Verlag, Berlin, 1979), Chap. 3, p. 55.
28. S. Havlin and D. Ben-Avraham, Adv. Phys. 36, 695 (1987)
29. B.P. Lee, J. Phys. A 27, 2633 (1994)
30. P.A. Alemany, D.H. Zanette, and H.S. Wio, Phys. Rev. E 50, 3646 (1994)
31. P.A. Alemany and H.S. Wio, ICTP Report No. IC/96/186, 1996 (unpublished);M.J. Howard and U.C. Täuber, (unpublished).
32. J. Bear, Dynamicas of Fluids in Porous Media (Elsevier, New York, 1972).
33. H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids (Oxford University Press, London, 1959).
34. L. Boltzmann, Ann. Phys. (Leipzig) 53, 959 (1894).
35. N. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1982)
36. C.W. Gardiner, Handbook of Stochastic Methods, 2nd ed. (Springer-Verlag, Berlin, 1985)
37. H.S. Wio, An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics (World Scientific, Singapore, 1994)
38. B.D. Hughes, Random Walks and Random Environments (Clarendon Press, Oxford, 1995), Vol. I.
39. C. Tsallis, Quim. Nova 17, 468 (1994)
40. E.P. Borges, J. Phys. A 31, 5281 (1998).
41. J. Klafter, M. Shlesinger, and G. Zumofen, Phys. Today 49, 33 (1996)
42. C. Tsallis, Phys. World 10, 42 (1997).