General solution of the diffusion equation with a nonlocal diffusive term and a linear force term

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 4, 2006, Pages

  Malacarne, L C ^a   Mendes, R S ^a   Lenzi, E K ^a   Lenzi, M K ^b  

^a STATE UNIVERSITY OF MARINGÁ   (Brazil)

^b FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; LINEAR EQUATIONS;

DIFFUSION EQUATIONS; DIFFUSIVE PROCESS; LINEAR EXTERNAL FORCE; SPATIAL KERNEL DEPENDENCE;

NONLINEAR EQUATIONS;

EID: 33750177917     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.042101     Document Type: Article

References (53)

1. A. Einstein, Ann. Phys. (Leipzig) ANPYA2 0003-3804 17, 549 (1905).
2. J. D. Seymour, J. P. Gage, S. L. Codd, and R. Gerlach, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.198103 93, 198103 (2004).
3. J. G. Berryman, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.523190 18, 2108 (1977).
4. T. Kosztolowicz, K. Dworecki, and S. Mrowczynski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.170602 94, 170602 (2005).
5. R. C. Lua and A. Y. Grosberg, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.061918 72, 061918 (2005).
6. H. G. E. Hentschel and I. Procaccia, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.29.1461 29, 1461 (1984).
7. A. Ott, J. P. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.2201 65, 2201 (1990).
8. H. Spohn, J. Phys. I JPGCE8 1155-4304 10.1051/jp1:1993117 3, 69 (1993).
9. T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.3975 71, 3975 (1993).
10. F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.203 72, 203 (1994).
11. H. E. Roman, Fractals FRACEG 0218-348X 10.1142/S0218348X0400246X 12, 149 (2004);
12. J. Stephenson, Physica A PHYADX 0378-4371 10.1016/0378-4371(95)00201-4 222, 234 (1995);
13. R. Metzler, W. G. Glöckle, and T. F. Nonnenmacher, Physica A PHYADX 0378-4371 10.1016/0378-4371(94)90064-7 211, 13 (1994).
14. O. V. Bychuk and B. O’Shaughnessy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.1795 74, 1795 (1995);
15. S. C. Venkataramani, T. M. Antonsen, and E. Ott, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.3864 78, 3864 (1997).
16. A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.5655 85, 5655 (2000).
17. Xiao-Lun Wu and A. Libchaber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.3017 84, 3017 (2000).
18. J. K. Lawrence, A. C. Cadavid, A. Ruzmaikin, and T. E. Berger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5894 86, 5894 (2001).
19. R. Hilfer, Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000).
20. R. Metzler and J. Klafter, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3 339, 1 (2000).
21. B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators (Springer, New York, 2002).
22. G. M. Zaslavsky, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(02)00331- 9 371, 461 (2002).
23. W. R. Schneider and W. Wyss, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.528578 30, 134 (1989).
24. R. Metzler and J. Klafter, Physica A PHYADX 0378-4371 10.1016/S0378-4371(99)00503-8 278, 107 (2000).
25. R. Metzler, E. Barkai, and J. Klafter, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i1999-00279-7 46, 431 (1999).
26. Y. E. Ryabov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.030102 68, 030102 (R) (2003).
27. V. V. Anh and N. N. Leonenko, Appl. Math. Comput. AMHCBQ 0096-3003 10.1016/S0096-3003(02)00322-3 141, 77 (2003).
28. E. Barkai and R. J. Silbey, J. Phys. Chem. B JPCBFK 1089-5647 10.1021/jp993491m 104, 3866 (2000).
29. F. Mainardi and G. Pagnini, Appl. Math. Comput. AMHCBQ 0096-3003 10.1016/S0096-3003(02)00320-X 141, 51 (2003).
30. B. N. N. Achar and J. W. Hanneken, J. Mol. Liq. JMLIDT 0167-7322 10.1016/j.molliq.2004.02.012 114, 147 (2004).
31. Fu-Yao Ren, Jin-Rong Liang, Wei-Yuan Qiu, Xiao-Tian Wang, Y. Xu, and R. R. Nigmatullin, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(03)00644-3 312, 187 (2003).
32. P. Agrawal, Nonlinear Dyn. NODYES 0924-090X 10.1023/A:1016539022492 29, 145 (2002).
33. S. A. El-Wakil and M. A. Zahran, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/S0960-0779(00)00149-1 12, 1929 (2001).
34. S. A. El-Wakil, A. Elhanbaly, and M. A. Zahran, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/S0960-0779(99)00203-9 12, 1035 (2001).
35. E. K. Lenzi, R. S. Mendes, Kwok Sau Fa, L. C. Malacarne, and L. R. da Silva, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1566452 44, 2179 (2003).
36. E. K. Lenzi, R. S. Mendes, J. S. Andrade, L. R. da Silva, and L. S. Lucena, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.052101 71, 052101 (2005).
37. P. C. Assis, R. P. de Souza, P. C. da Silva, L. R. da Silva, L. S. Lucena, and E. K. Lenzi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73. 032101 73, 032101 (2006).
38. A. V. Chechkin, R. Gorenflo, and I. M. Sokolov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.046129 66, 046129 (2002).
39. I. M. Sokolov, A. V. Chechkin, and J. Klafter, Physica A PHYADX 0378-4371 10.1016/j.physa.2003.12.044 336, 245 (2004).
40. M. M. Meerschaert, D. A. Benson, and B. Baeumer, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.021112 63, 021112 (2001).
41. M. F. Shlesinger, B. J. West, and J. Klafter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.1100 58, 1100 (1987);
42. J. Klafter, A. Blumen, and M. F. Shlesinger, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.35.3081 35, 3081 (1987).
43. J.-P. Bouchaud and A. Georges, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(90)90099-N 195, 127 (1990).
44. D. A. Benson, R. Schumer, S. W. Wheatcraft, and M. M. Meerschaert, Transp. Porous Media TPMEEI 0169-3913 10.1023/A:1006733002131 42, 211 (2001).
45. I. M. Sokolov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.041101 66, 041101 (2002).
46. T. Kosztolowicz, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/45/005 37, 10779 (2004).
47. A. M. Mathai and R. K. Saxena, The H-function with Application in Statistics and Other Disciplines (Wiley Eastern, New Delhi, 1978).
48. H. Risken, The Fokker-Planck Equation, Methods of Solution and Applications (Springer-Verlag, New York, 1984).
49. S. Jespersen, R. Metzler, and H. C. Fogedby, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.2736 59, 2736 (1999).
50. L. C. Malacarne, R. S. Mendes, I. T. Pedron, and E. K. Lenzi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.052101 65, 052101 (2002).
51. L. C. Malacarne, R. S. Mendes, I. T. Pedron, and E. K. Lenzi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.030101 63, 030101 (R) (2001).
52. I. M. Sokolov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.056111 63, 056111 (2001);
53. I. M. Sokolov, J. Klafter, and A. Blumen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.021107 64, 021107 (2001).