J. M. Ball, J. Carr, and O. Penrose, The Becker-Döring cluster equations: basic properties and asymptotic behaviour of solutions, Comm. Math. Phys, vol.104, issue.4, pp.657-692, 1986.

R. Becker and W. Döring, Kinetische behandlung der keimbildung in bersttigten dmpfen, Annalen der Physik, vol.416, issue.8, pp.719-752, 1935.

M. F. Bishop and F. A. Ferrone, Kinetics of nucleation-controlled polymerization. a perturbation treatment for use with a secondary pathway, Biophysical Journal, vol.46, issue.5, pp.631-644, 1984.

V. Calvez, M. Doumic, and P. Gabriel, Self-similarity in a general aggregationfragmentation problem. application to fitness analysis, Journal de Mathmatiques Pures et Appliques, vol.98, issue.1, pp.1-27, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00539279

V. Calvez, N. Lenuzza, M. Doumic, J. Deslys, F. Mouthon et al., Prion dynamic with size dependency-strain phenomena, J. of Biol. Dyn, vol.4, issue.1, pp.28-42, 2010.

J. Collet, T. Goudon, F. Poupaud, and A. Vasseur, The Becker-Döring system and its Lifshitz-Slyozov limit, SIAM J. on Appl. Math, vol.62, issue.5, pp.1488-1500, 2002.

J. Collet and T. Goudon, On solutions of the LifshitzSlyozov model, Nonlinearity, vol.13, issue.4, pp.1239-1262, 2000.

J. Collet, T. Goudon, and A. Vasseur, Some remarks on large-time asymptotic of the Lifshitz-Slyozov equations, J. Statist. Phys, vol.108, issue.1-2, pp.341-359, 2002.

J. F. Collet and S. Hariz, A modified version of the lifshitz-slyozov model, Applied Mathematics Letters, vol.12, pp.81-95, 1999.

J. Deschamps, E. Hingant, and R. Yvinec, Quasi steady state approximation of the small clusters in becker-döring equations leads to boundary conditions in the lifshitz-slyozov limit, Communications in Mathematical Sciences, vol.15, issue.5, pp.1353-1384, 2017.

M. Doumic and P. Gabriel, Eigenelements of a general aggregationfragmentation model, Mathematical Models and Methods in Applied Sciences, vol.20, issue.05, p.757, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00408088

M. Doumic, T. Goudon, and T. Lepoutre, Scaling Limit of a Discrete Prion Dynamics Model, Comm. in Math. Sc, vol.7, issue.4, pp.839-865, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00403914

M. Escobedo, S. Mischler, and B. Perthame, Gelation in coagulation and fragmentation models, Comm. Math. Phys, vol.231, issue.1, pp.157-188, 2002.

F. Filbet and P. Laurençot, Numerical approximation of the LifshitzSlyozov-Wagner equation, SIAM J. Numer. Anal, vol.41, issue.2, pp.563-588, 2003.

P. Gabriel, Global stability for the prion equation with general incidence, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01002824

M. L. Greer, L. Pujo-menjouet, and G. F. Webb, A mathematical analysis of the dynamics of prion proliferation, J. Theoret. Biol, vol.242, issue.3, pp.598-606, 2006.

P. Laurençot, Weak solutions to the lifshitz-slyozov-wagner equation, Indiana University Mathematical Journal, vol.50, pp.1319-1346, 2001.

P. Laurençot and C. Walker, Well-posedness for a model of prion proliferation dynamics, J. Evol. Equ, vol.7, issue.2, pp.241-264, 2007.

P. Laurençot, Steady states for a fragmentation equation with size diffusion, vol.66, pp.211-219, 2004.

I. M. Lifshitz and V. V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, Journal of Physics and Chemistry of Solids, vol.19, issue.12, pp.35-50, 1961.
DOI : 10.1016/0022-3697(61)90054-3

P. Michel, Optimal proliferation rate in a cell division model, Math. Model. Nat. Phenom, vol.1, issue.2, pp.23-44, 2006.
DOI : 10.1051/mmnp:2008002
URL : https://www.mmnp-journal.org/articles/mmnp/pdf/2006/02/mmnp2006202.pdf

P. Michel, A singular asymptotic behavior of a transport equation, C.R. Acad. Sci, vol.346, pp.155-159, 2008.
DOI : 10.1016/j.crma.2007.12.010

B. Niethammer, Derivation of the LSW-theory for Ostwald ripening by homogenization methods, Arch. Ration. Mech. Anal, vol.147, issue.2, pp.119-178, 1999.

B. Niethammer and R. L. Pego, Non-self-similar behavior in the LSW theory of Ostwald ripening, J. Statist. Phys, vol.95, pp.867-902, 1999.

B. Niethammer and R. L. Pego, On the initial-value problem in the Lifshitz-Slyozov-Wagner theory of Ostwald ripening, SIAM J. Math. Anal, vol.31, issue.3, pp.467-485, 2000.

B. Niethammer and R. L. Pego, The LSW model for domain coarsening: asymptotic behavior for conserved total mass, J. Statist. Phys, vol.104, pp.1113-1144, 2001.

B. Niethammer and J. J. Velázquez, On the convergence to the smooth self-similar solution in the LSW model, Indiana Univ. Math. J, vol.55, issue.2, pp.761-794, 2006.

O. Penrose, Metastable states for the becker-döring cluster equations, Communications in Mathematical Physics, vol.124, issue.4, pp.515-541, 1989.
DOI : 10.1007/bf01218449

B. Perthame, Transport equations in biology, Frontiers in Mathematics, 2007.

S. Prigent, A. Ballesta, F. Charles, N. Lenuzza, P. Gabriel et al., An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation, PLoS ONE, vol.7, issue.11, p.43273, 2012.
DOI : 10.1371/journal.pone.0043273
URL : https://hal.archives-ouvertes.fr/hal-00778052

J. Pruss, L. Pujo-menjouet, G. F. Webb, and R. Zacher, Analysis of a model for the dynamics of prion, Dis. Cont. Dyn. Sys. Ser. B, vol.6, issue.1, pp.225-235, 2006.

G. Simonett and C. Walker, On the solvability of a mathematical model for prion proliferation, J. Math. Anal. Appl, vol.324, issue.1, p.580, 2006.