A Elhanbaly 2003 J. Phys. A: Math. Gen. 36 8311 doi:10.1088/0305-4470/36/30/308
A Elhanbaly
Show affiliationsIn this paper we obtain a complete classification of all possible non-trivial similarity solutions of the integro–differential fragmentation equation with continuous mass loss rate. These solutions include the effects of both continuous and discrete mass loss rates. The similarity solutions are compared with the solutions found earlier. The comparison shows that some previous solutions are obtained as special cases from our solutions. The results reported here provide further evidence of the usefulness of the Lie group method for obtaining similarity solutions for either differential or integro–differential equations.
45K05 Integro-partial differential equations (See also 34K30, 35R10, 47G20)
Issue 30 (1 August 2003)
Received 19 November 2002, in final form 13 May 2003
Published 16 July 2003
A Elhanbaly 2003 J. Phys. A: Math. Gen. 36 8311
S Muñoz San Martín et al 2003 Phys. Med. Biol. 48 1649
G J Clerk and B H J McKellar 1992 J. Phys. A: Math. Gen. 25 L861
L Cesnak et al 2000 Supercond. Sci. Technol. 13 1461
Mingli Chen et al 2008 Phys. Med. Biol. 53 5513
O Sarbach and E Winstanley 2001 Class. Quantum Grav. 18 2125
Jean-Pierre Amiet and Stefan Weigert 1999 J. Phys. A: Math. Gen. 32 2777
Jacek Rożynek and Grzegorz Wilk 2009 J. Phys. G: Nucl. Part. Phys. 36 125108
M J Martínez-Pérez et al 2009 Supercond. Sci. Technol. 22 125020
S Graffi and F Unguendoli 1994 J. Phys. A: Math. Gen. 27 4281