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All issues Volume 55 / No 5 (September-October 2021) ESAIM: M2AN, 55 5 (2021) 2473-2501 References
Open Access
Issue
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
Page(s) 2473 - 2501
DOI https://doi.org/10.1051/m2an/2021061
Published online 26 October 2021
  1. A.S. Ackleh, Parameter estimation in a structured algal coagulation-fragmentation model. Nonlinear Anal.: Theory Methods App. 28 (1997) 837–854. [CrossRef] [Google Scholar]
  2. A.S. Ackleh and K. Deng, A nonautonomous juvenile-adult model: well-posedness and long-time behavior via a comparison principle. SIAM J. Appl. Math. 69 (2009) 1644–1661. [CrossRef] [MathSciNet] [Google Scholar]
  3. A.S. Ackleh and B.G. Fitzpatrick, Modeling aggregation and growth processes in an algal population model: analysis and computations. J. Math. Biol. 35 (1997) 480–502. [CrossRef] [MathSciNet] [Google Scholar]
  4. A.S. Ackleh and R.L. Miller, A model for the interaction of phytoplankton aggregates and the environment: approximation and parameter estimation. Inverse Prob. Sci. Eng. 26 (2017) 152–182. [Google Scholar]
  5. A.S. Ackleh and N. Saintier, Well-posedness for a system of transport and diffusion equations in measure spaces. J. Math. Anal. App. 492 (2020) 1–32. [Google Scholar]
  6. A.S. Ackleh and N. Saintier, Diffusive limit to a selection-mutation equation with small mutation formulated on the space of measures. Discrete Continuous Dyn. Syst. Ser. B 26 (2021) 1469. [CrossRef] [MathSciNet] [Google Scholar]
  7. A.S. Ackleh, K. Deng and X. Wang, Existence-uniqueness and monotone approximation for a phytoplankton-zooplankton aggregation model. Z. Angew. Math. Phys. 57 (2006) 733–749. [CrossRef] [MathSciNet] [Google Scholar]
  8. A.S. Ackleh, J. Carter, K. Deng, Q. Huang, N. Pal and X. Yang, Fitting a structured juvenile-adult model for green tree frogs to population estimates from capture-mark-recapture field data. Bull. Math. Biol. 74 (2012) 641–665. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  9. A.S. Ackleh, R. Lyons and N. Saintier, Finite difference schemes for a structured population model in the space of measures. Math. Biosci. Eng. MBE 17 (2020) 747–775. [CrossRef] [Google Scholar]
  10. J.M. Ball and J. Carr, The discrete coagulation-fragmentation equations: existence, uniqueness, and density conservation. J. Stat. Phys. 61 (1990) 203–234. [CrossRef] [Google Scholar]
  11. J. Banasiak and W. Lamb, Coagulation, fragmentation and growth processes in a size structured population. Discrete Continuous Dyn. Syst.-Ser. B 11 (2009) 563–585. [CrossRef] [MathSciNet] [Google Scholar]
  12. R.J.H. Beverton and S.J. Holt, On the dynamics of exploited fish populations. In: Fisheries and Food. Vol. XIX of Fishery Investigations Series II. Ministry of Agriculture (1957) 1–957. [Google Scholar]
  13. P.J. Blatz and A.V. Tobolsky, Note on the kinetics of systems manifesting simultaneous polymerization-depolymerization phenomena. J. Phys. Chem. 49 (1945) 77–80. [CrossRef] [Google Scholar]
  14. J.P. Bourgade and F. Filbet, Convergence of a finite volume scheme for coagulation-fragmentation equations. Math. Comput. 77 (2008) 851–882. [Google Scholar]
  15. A.B. Burd and G.A. Jackson, Particle aggregation. Ann. Rev. Mar. Sci. 1 (2009) 65–90. [CrossRef] [PubMed] [Google Scholar]
  16. J.A. Cañizo, Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance. J. Stat. Phys. 129 (2007) 1–26. [CrossRef] [MathSciNet] [Google Scholar]
  17. J.A. Cañizo, J.A. Carrillo and S. Cuadrado, Measure solutions for some models in population dynamics. Acta Appl. Math. 123 (2013) 141–156. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. Carrillo, R.M. Colombo, P. Gwiazda and A. Ulikowska, Structured populations, cell growth and measure valued balance laws. J. Differ. Equ. 252 (2012) 3245–3277. [CrossRef] [Google Scholar]
  19. J.M.C. Clark and V. Katsouros, Stably coalescent stochastic froths. Adv. Appl. Probab. 31 (1999) 199–219. [CrossRef] [MathSciNet] [Google Scholar]
  20. T. Debiec, M. Doumic, P. Gwiazda and E. Wiedemann, Relative entropy method for measure solutions of the growth-fragmentation equation. SIAM J. Math. Anal. 50 (2018) 5811–5824. [CrossRef] [MathSciNet] [Google Scholar]
  21. K. Deng and Y. Wu, Extinction and uniform strong persistence of a size-structured population model. Discrete Continuous Dyn. Syst. Ser. B 22 (2017) 831–840. [CrossRef] [MathSciNet] [Google Scholar]
  22. R.M. Dudley, Distances of probability measures and random variables. In: Selected Works of RM Dudley. Springer (2010) 28–37. [CrossRef] [Google Scholar]
  23. A. Eibeck and W. Wagner, Approximative solution of the continuous coagulation-fragmentation equation. Stochastic Anal. App. 18 (2000) 921–948. [CrossRef] [Google Scholar]
  24. J.H. Evers, S.C. Hille and A. Muntean, Mild solutions to a measure-valued mass evolution problem with flux boundary conditions. J. Differ. Equ. 259 (2015) 1068–1097. [CrossRef] [Google Scholar]
  25. H. Federer, Geometric Measure Theory. Springer (2014). [Google Scholar]
  26. H. Federer, Colloquium lectures on geometric measure theory. Bull. Am. Math. Soc. 84 (1978) 291–338. [CrossRef] [Google Scholar]
  27. R. Fortet and E. Mourier, Convergence de la Répartition Empirique Vers la Répartition Théorique. Annales scientifiques de l’École Normale Supérieure 70 (1953) 267–285. [CrossRef] [Google Scholar]
  28. A.K. Giri, J. Kumar and G. Warnecke, The continuous coagulation equation with multiple fragmentation. J. Math. Anal. App. 374 (2011) 71–87. [CrossRef] [Google Scholar]
  29. A.K. Giri, P. Laurençot and G. Warnecke, Weak solutions to the continuous coagulation equation with multiple fragmentation. Nonlinear Anal. Theory Methods App. 75 (2012) 2199–2208. [CrossRef] [Google Scholar]
  30. P. Gwiazda and A. Marciniak-Czochra, Structured population equations in metric spaces. J. Hyperbolic Differ. Equ. 07 (2010) 733–773. [CrossRef] [Google Scholar]
  31. P. Gwiazda, T. Lorenz and A. Marciniak-Czochra, A Nonlinear structured population model: Lipschitz continuity of measure-valued solutions with respect to model ingredients. J. Differ. Equ. 248 (2010) 2703–2735. [CrossRef] [Google Scholar]
  32. P. Gwiazda, A. Marciniak-Czochra and H.R. Thieme, Measures under the flat norm as ordered normed vector space. Positivity 22 (2017) 105–138. [Google Scholar]
  33. O.J. Heilmann, Analytical solutions of Smoluchowski’s coagulation equation. J. Phys. A 25 (1992) 3763–3771. [Google Scholar]
  34. J. Jabłoński and A. Marciniak-Czochra, Efficient algorithms computing distances between Radon measures on ℝ. Preprint arXiv:1304.3501 (2013). [Google Scholar]
  35. J. Jabłoński and D. Wrzosek, Measure-valued solutions to size-structured population model of prey controlled by optimally foraging predator harvester. Math. Models Methods Appl. Sci. 29 (2019) 1657–1689. [CrossRef] [MathSciNet] [Google Scholar]
  36. G.A. Jackson, A model of the formation of marine algal flocs by physical coagulation processes. Deep Sea Res. Part A. Oceanogr. Res. Papers 37 (1990) 1197–1211. [CrossRef] [Google Scholar]
  37. G.A. Jackson and S.E. Lochmann, Effect of coagulation on nutrient and light limitation of an algal bloom. Limnol. Oceanogr. 37 (1992) 77–89. [CrossRef] [Google Scholar]
  38. I. Jeon, Existence of getting solutions for coagulation-fragmentation equations. Commun. Math. Phys. 194 (1998) 541–567. [CrossRef] [Google Scholar]
  39. D.D. Keck and D.M. Bortz, Numerical simulation of solutions and moments of the Smoluchowski coagulation equation., Preprint arXiv:1312.7240 (2013). [Google Scholar]
  40. W. Lamb, Existence and uniqueness results for the continuous coagulation and fragmentation equation. Math. Models Methods Appl. Sci. 27 (2004) 703–721. [CrossRef] [Google Scholar]
  41. A. Lasota, J. Myjak and T. Szarek, Markov operators with a unique invariant measure. J. Math. Anal. App. 276 (2002) 343–356. [CrossRef] [Google Scholar]
  42. P. Laurençot, On a class of continuous coagulation–fragmentation equations. J. Differ. Equ. 167 (2000) 245–274. [CrossRef] [Google Scholar]
  43. P. Laurençot and S. Mischler, Global existence for the discrete diffusive coagulation–fragmentation equations in L1. Rev. Mat. Iberoam. 18 (2002) 731–745. [CrossRef] [Google Scholar]
  44. P. Laurençot and S. Mischler, From the discrete to the continuous coagulation fragmentation equations. Proc. R. Soc. Edinburgh Sect. A: Math. 132 (2002) 1219–1248. [CrossRef] [Google Scholar]
  45. P. Laurençot and S. Mischler, On coalescence equations and related models, edited by P. Degond, L. Pareschi and G. Russo. In: Modeling and Computational Methods for Kinetic Equations. Boston, Birkhäuser (2004) 321–356. [CrossRef] [Google Scholar]
  46. H. Liu, R. Gröpler and G. Warnecke, A high order positivity preserving DG method for coagulation–fragmentation equations. SIAM J. Sci. Comput. 41 (2019) 448–465. [Google Scholar]
  47. D.J. McLaughlin, W. Lamb and A.C. McBride, An existence and uniqueness result for a coagulation and multiple-fragmentation equation. SIAM J. Math. Anal. 28 (1997) 1173–1190. [CrossRef] [MathSciNet] [Google Scholar]
  48. Z.A. Melzak, A scalar transport equation. Trans. Am. Math. Soc. 85 (1957) 547–560. [CrossRef] [Google Scholar]
  49. H. Müller, Zur Allgemeinen Theorie der Raschen Koagulation. Fortschrittsberichte über Kolloide und Polymere 27 (1928) 223–250. [CrossRef] [Google Scholar]
  50. J.R. Norris, Smoluchowski’s coagulation equation: uniqueness, non-uniqueness and a hydrodynamic limit for the stochastic coalescent. Ann. Appl. Probab. 9 (1999) 78–109. [CrossRef] [MathSciNet] [Google Scholar]
  51. D. Pauly and G.R. Morgan, Length-Based Methods in Fisheries Research. WorldFish 13 (1987). [Google Scholar]
  52. W.E. Ricker, Stock and recruitment. J. Fisheries Board Can. 11 (1954) 559–623. [CrossRef] [Google Scholar]
  53. R. Rudnicki and R. Wieczorek, Fragmentation-coagulation models of phytoplankton. Bull. Polish Acad. Sci. Math. 54 (2006) 175–191. [CrossRef] [MathSciNet] [Google Scholar]
  54. R. Singh, J. Saha and J. Kumar, Adomian decomposition method for solving fragmentation and aggregation population balance equations. J. Appl. Math. Comput. 48 (2014) 265–292. [Google Scholar]
  55. M. Smoluchowski, Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen. Phys. Z. 17 (1916) 557–571, 585–599. [Google Scholar]
  56. I.W. Stewart, A global existence theorem for the general coagulation–fragmentation equation with unbounded kernels. Math. Methods Appli. Sci. 11 (1989) 627–648. [CrossRef] [Google Scholar]

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