Discrete coagulation-fragmentation system with transport and diffusion

Stéphane Brull[1]

  • [1] ANLA, University of Toulon, avenue de l’université, 83957 La Garde, France.

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 3, page 439-460
  • ISSN: 0240-2963

Abstract

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We prove the existence of solutions to two infinite systems of equations obtained by adding a transport term to the classical discrete coagulation-fragmentation system and in a second case by adding transport and spacial diffusion. In both case, the particles have the same velocity as the fluid and in the second case the diffusion coefficients are equal. First a truncated system in size is solved and after we pass to the limit by using compactness properties.

How to cite

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Brull, Stéphane. "Discrete coagulation-fragmentation system with transport and diffusion." Annales de la faculté des sciences de Toulouse Mathématiques 17.3 (2008): 439-460. <http://eudml.org/doc/10092>.

@article{Brull2008,
abstract = {We prove the existence of solutions to two infinite systems of equations obtained by adding a transport term to the classical discrete coagulation-fragmentation system and in a second case by adding transport and spacial diffusion. In both case, the particles have the same velocity as the fluid and in the second case the diffusion coefficients are equal. First a truncated system in size is solved and after we pass to the limit by using compactness properties.},
affiliation = {ANLA, University of Toulon, avenue de l’université, 83957 La Garde, France.},
author = {Brull, Stéphane},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {existence; compactness},
language = {eng},
month = {6},
number = {3},
pages = {439-460},
publisher = {Université Paul Sabatier, Toulouse},
title = {Discrete coagulation-fragmentation system with transport and diffusion},
url = {http://eudml.org/doc/10092},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Brull, Stéphane
TI - Discrete coagulation-fragmentation system with transport and diffusion
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 3
SP - 439
EP - 460
AB - We prove the existence of solutions to two infinite systems of equations obtained by adding a transport term to the classical discrete coagulation-fragmentation system and in a second case by adding transport and spacial diffusion. In both case, the particles have the same velocity as the fluid and in the second case the diffusion coefficients are equal. First a truncated system in size is solved and after we pass to the limit by using compactness properties.
LA - eng
KW - existence; compactness
UR - http://eudml.org/doc/10092
ER -

References

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  1. Aman (H.).— Coagulation-fragmentation processes Arch. Ration. Mech. Anal. 151, p. 339-366 (2000). Zbl0977.35060MR1756908
  2. Ball (J.M.), Carr (J.).— The discrete coagulation-fragmentation equations : existence, uniqueness and density conservation. Journ.stat.phys., 61, p. 203-234 (1990). Zbl1217.82050MR1084278
  3. Ball (J.M.), Carr (J.), Penrose (O.).— The Becker-Doring Cluster Equations : Basic Properties and asymptotic Behaviour of Solutions. Comm. Math. Phys., 104, p. 657-692 (1986). Zbl0594.58063MR841675
  4. Burobin (A.V.).— Existence and uniqueness of a solution of a Cauchy Problem for inhomogeneous three-dimentional coagulation. differential equations 19, p. 1187-1197 (1983). Zbl0553.35072MR718559
  5. Chae (D.), Dubovskii (P.).— Existence and uniqueness for spacially inhomogeneous coagulation-condensation equation with unbounded kernels Journ. of integral equations vol 9, No 3, p. 279-236 (1997). Zbl0907.45010MR1616462
  6. Collet (J.F.), Poupaud (F.).— Asymptotic behaviour of solutions to the diffusive fragmentation-coagulation system. Physica D vol.114, p. 123-146 (1998). Zbl0960.82017MR1612051
  7. Collet (J.F.), Poupaud (F.).— Existence of solutions to coagulation-fragmentation systems with diffusion. Transp. Theory. Stat. Phys. 25, p. 503-513 (1996). Zbl0870.35117MR1407550
  8. Dubovskii (P.B.).— Existence theorem for space inhomogeneous coagulation equation. Differential equations 26, p. 508-513 (1990). 
  9. Guyon (E.).— Hydrodynamique Physique. édition EDP Sciences (2001). 
  10. Laurencot (P.), Mischler (S.).— Global existence for the discrete diffusive coagulation-fragmentation equations in L 1 . Rev.Mat.Iberoaericana 18, p. 221-235 (2002). Zbl1036.35089MR1954870
  11. Laurencot (P.), Mischler (S.).— The continous coagulation-fragmentation equations with diffusion. Arch.Rational Mech. Anal. 162 No1, p. 45-99 (2002). Zbl0997.45005MR1892231
  12. Laurencot (P.), Mischler (S.).— From the discrete to the continous coagulation-fragmentation equations. Proc. Roy. Soc. Edinburgh 132A, p. 1219-1248 (2002). Zbl1034.35011MR1938720
  13. Simon (J.).— Compact sets in L p ( 0 , T , B ) , Ann. Mat. Pura. Appl., IV 146, p. 65-96 (1987). Zbl0629.46031MR916688
  14. Slemrod (M.).— Coagulation-diffusion : derivation and existence of solutions for the diffuse interface stucture equations. Physica D, 46 (3), p. 351-366 (1990). Zbl0732.35103MR1081687

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