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All issues Volume 55 / No 3 (May-June 2021) ESAIM: M2AN, 55 3 (2021) 1067-1101 References
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Issue
ESAIM: M2AN
Volume 55, Number 3, May-June 2021
Page(s) 1067 - 1101
DOI https://doi.org/10.1051/m2an/2020088
Published online 08 June 2021
  1. M. Aizenman and T.A. Bak, Convergence to equilibrium in a system of reacting polymers. Comm. Math. Phys. 65 (1979) 203–230. [Google Scholar]
  2. W. Arendt, C.J.K. Batty, M. Hieber and F. Neubrander, Vector-valued laplace transforms and Cauchy Problems. In: Monographs in Mathematics. Birkhauser Verlag (2001). [Google Scholar]
  3. H. Babovsky, On a Monte Carlo approach to the Smoluchowski equations,. Monte Carlo Methods App. 5 (1999) 1–18. [Google Scholar]
  4. G. Baird, Mixed discrete–continuous fragmentation equations. Ph.D. thesis, University of Oxford (2017). https://ora.ox.ac.uk/objects/uuid:311da0da-6801-4120-9129-d95786a153b6. [Google Scholar]
  5. G. Baird and E. Süli, A mixed discrete–continuous fragmentation model. J. Math. Anal. App. 473 (2019) 273–296. [Google Scholar]
  6. J. Banasiak, On an extension of Kato-Voigt perturbation theorem for substochastic semigroups and its application. Taiwanese J. Math. 5 (2001) 169–191. [Google Scholar]
  7. J. Banasiak, Transport processes with coagulation and strong fragmentation. Discrete Contin. Dyn. Syst. B 17 (2012) 445–472. [Google Scholar]
  8. J. Banasiak and L. Arlotti, Perturbations of Positive Semigroups with Applications. Springer-Verlag, London (2006). [Google Scholar]
  9. J. Banasiak and W. Lamb, On the application of substochastic semigroup theory to fragmentation models with mass loss. J. Math. Anal. Appl. 284 (2003) 9–30. [Google Scholar]
  10. J. Banasiak and W. Lamb, Coagulation, fragmentation and growth processes in a size structured population. Discrete Contin. Dyn. Syst. Ser. B 11 (2009) 563–585. [Google Scholar]
  11. J. Banasiak and W. Lamb, Analytic fragmentation semigroups and continuous coagulation–fragmentation equations with unbounded rates. J. Math. Anal. App. 391 (2012) 312–322. [Google Scholar]
  12. J. Banasiak and W. Lamb, The discrete fragmentation equations: semigroups, compactness and asynchronous exponential growth. Kinetic Related Models 5 (2012) 223–236. [Google Scholar]
  13. J. Banasiak and W. Lamb, On the existence of moments of solutions to fragmentation equations. J. Math. Anal. App. 413 (2014) 1017–1029. [Google Scholar]
  14. J. Banasiak, W. Lamb and M. Langer, Strong fragmentation and coagulation with power-law rates. J. Eng. Math. 82 (2013) 199–215. [Google Scholar]
  15. J. Banasiak, L.O. Joel and S. Shindin, Analysis and simulations of the discrete fragmentation equation with decay. Math. Methods Appl. Sci. 41 (2018) 6530–6545. [Google Scholar]
  16. J.C. Barrett and J.S. Jheeta, Improving the accuracy of the moments method for solving the aerosol general dynamic equation. J. Aerosol Sci. 27 (1996) 1135–1142. [Google Scholar]
  17. P.N. Blair, W. Lamb and I.W. Stewart, Coagulation and fragmentation with discrete mass loss. J. Math. Anal. Appl. 329 (2007) 1285–1302. [Google Scholar]
  18. J.P. Bourgade and F. Filbet, Convergence of a finite volume scheme for coagulation–fragmentation equations. Math. Comp. 77 (2008) 851–882. [Google Scholar]
  19. J.A. Canizo, Evolution equations in a Banach space (2006). http://canizo.org/tex/evolution.pdf. [Google Scholar]
  20. M.E. Costas, M. Moreau and L. Vicente, Some analytical and numerical solutions for colloidal aggregation with fragmentation. J. Phys. A: Math. General 28 (1995) 2981–2994. [Google Scholar]
  21. P. Degond and M. Engel, Numerical approximation of a coagulation–fragmentation model for animal group size statistics. Netw. Heterogeneous Media 12 (2017) 217–243. [Google Scholar]
  22. P. Degond, J.-G. Liu and R.L. Pego, Coagulation–fragmentation model for animal group-size statistics. J. Nonlinear Sci. 27 (2017) 379–424. [Google Scholar]
  23. J. Drazkowska, F. Windmark and C.P. Dullemond, Modeling dust growth in protoplanetary disks: the breakthrough case. Astron. Astrophys. 567 (2014) A38. [Google Scholar]
  24. A. Eibeck and W. Wagner, An efficient stochastic algorithm for studying coagulation dynamics and gelation phenomena. SIAM J. Sci. Comput. 22 (2000) 802–821. [CrossRef] [Google Scholar]
  25. K.J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations. Springer, New York (2000). [Google Scholar]
  26. F. Filbet, An asymptotically stable scheme for diffusive coagulation–fragmentation models. Commun. Math. Sci. 6 (2008) 257–280. [Google Scholar]
  27. F. Filbet and P. Laurençot, Numerical simulation of the Smoluchowski coagulation equation. SIAM J. Sci. Comput. 25 (2004) 2004–2028. [CrossRef] [Google Scholar]
  28. A.F. Filippov, On the distribution of the sizes of particles which undergo splitting. Theory Probab. App. 6 (1961) 275–294. [Google Scholar]
  29. I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: Lp Spaces. Springer, New York (2007). [Google Scholar]
  30. L. Forestier-Coste and S. Mancini, A finite volume preserving scheme on nonuniform meshes and for multidimensional coalescence. SIAM J. Sci. Comput. 34 (2012) B840–B860. [Google Scholar]
  31. F. Guias, A Monte Carlo approach to the Smoluchowski equations. Monte Carlo Methods App. 3 (1997) 313–326. [Google Scholar]
  32. A. Johansen, F. Brauer, C. Dullemond and H. Klahr, A coagulation–fragmentation model for the turbulent growth and destruction of preplanetesimals. Astron. Astrophys. 486 (2008) 597–611. [Google Scholar]
  33. J. Kumar, J. Saha and E. Tsotsas, Development and convergence analysis of a finite volume scheme for solving breakage equation. SIAM J. Numer. Anal. 53 (2015) 1672–1689. [Google Scholar]
  34. R. Kumar, Numerical analysis of finite volume schemes for population balance equations. Ph.D. thesis, Otto-von-Guericke University Magdeburg (2010). https://www.researchgate.net/publication/50870176_Numerical_analysis_for_finite_volume_schemes_for_population_balance_equations. [Google Scholar]
  35. S. Kumar and D. Ramkrishna, On the solution of population balance equations by discretization–I. A fixed pivot technique. Chem. Eng. Sci. 51 (1996) 1311–1332. [CrossRef] [Google Scholar]
  36. R. Kumar, J. Kumar and G. Warnecke, Moment preserving finite volume schemes for solving population balance equations incorporating aggregation, breakage, growth and source terms. Math. Models Methods Appl. Sci. 23 (2013) 1235–1273. [Google Scholar]
  37. R. Kumar, J. Kumar and G. Warnecke, Convergence analysis of a finite volume scheme for solving non-linear aggregation-breakage population balance equations. Kinet. Related Models 7 (2014) 713–737. [Google Scholar]
  38. W. Lamb, Existence and uniqueness results for the continuous coagulation and fragmentation equation. Math. Meth. Appl. Sci. 27 (2004) 703–721. [CrossRef] [Google Scholar]
  39. P. Laurençot, Weak compactness techniques and coagulation equations. In: Vol. 2126 of Evolutionary Equations with Applications in Natural Sciences. Lecture Notes in Math. Springer International Publishing (2015) 199–253. [Google Scholar]
  40. E.H. Lieb and M. Loss, Analysis. Graduate Studies in Mathematics. American Mathematical Society (2001). [Google Scholar]
  41. A.C. McBride, A.L. Smith and W. Lamb, Strongly differentiable solutions of the discrete coagulation–fragmentation equation. Phys. D: Nonlinear Phenom. 239 (2010) 1436–1445. [Google Scholar]
  42. E.D. McGrady and R.M. Ziff, Shattering transition in fragmentation. Phys. Rev. Lett. 58 (1987) 892–895. [CrossRef] [PubMed] [Google Scholar]
  43. D.J. McLaughlin, W. Lamb and A.C. McBride, An existence and uniqueness theorem for a coagulation and multiple-fragmentation equation. SIAM J. Math. Anal. 28 (1997) 1173–1190. [CrossRef] [MathSciNet] [Google Scholar]
  44. D.J. McLaughlin, W. Lamb and A.C. McBride, A semigroup approach to fragmentation models. SIAM J. Math. Anal. 28 (1997) 1158–1172. [CrossRef] [MathSciNet] [Google Scholar]
  45. R. Nagel, Towards a matrix theory for unbounded operator matrices. Math. Z. 201 (1989) 57–68. [Google Scholar]
  46. M. Nicmanis and M.J. Hounslow, A finite element analysis of the steady state population balance equation for particulate systems: aggregation and growth. Comput. Chem. Eng. 20 (1996) S261–S266. [Google Scholar]
  47. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983). [Google Scholar]
  48. S. Qamar and G. Warnecke, Solving population balance equations for two-component aggregation by a finite volume scheme. Chem. Eng. Sci. 62 (2007) 679–693. [Google Scholar]
  49. S. Qamar, G. Warnecke and M.P. Elsner, On the solution of population balances for nucleation, growth, aggregation and breakage processes. Chem. Eng. Sci. 64 (2009) 2088–2095. [Google Scholar]
  50. J. Saha, N. Das, J. Kumar and A. Bück, Numerical solutions for multidimensional fragmentation problems using finite volume methods. Kinet. Related Models 12 (2019) 79–103. [Google Scholar]
  51. A.P. Smirnov, S.A. Matveev, D.A. Dmitry, A. Zheltkov and E.E. Tyrtyshnikov, Fast and accurate finite-difference method solving multicomponent Smoluchowski coagulation equation with source and sink terms. Proc. Comput. Sci. 80 (2016) 2141–2146. [Google Scholar]
  52. L. Smith, W. Lamb, M. Langer and A.C. McBride, Discrete fragmentation with mass loss. J. Evol. Equ. 12 (2012) 181–201. [Google Scholar]
  53. I.W. Stewart, A global existence theorem for the general coagulation–fragmentation equation with unbounded kernels. Math. Methods Appl. Sci. 11 (1989) 627–648. [Google Scholar]
  54. J. Voigt, On substochastic C0-semigroups and their generators. Trans. Theo. Stat. Phys. 16 (1987) 453–466. [Google Scholar]
  55. R.M. Ziff, Kinetics of polymerization. J. Stat. Phys. 23 (1980) 241–263. [CrossRef] [Google Scholar]

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