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Fragmentation-coagulation models of phytoplankton

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present two new models of the dynamics of phytoplankton aggregates. The first one is an individual-based model. Passing to infinity with the number of individuals, we obtain an Eulerian model. This model describes the evolution of the density of the spatial-mass distribution of aggregates. We show the existence and uniqueness of solutions of the evolution equation.
Rocznik
Strony
175--191
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
autor
  • Rudnicki Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland, rudnicki@us.edu.pl
Bibliografia
  • [1] A. S. Ackleh and K. Deng, On the first order hyperbolic coagulation model, Math. Methods Appl. Sci. 26 (2003), 703-715.
  • [2] R. Adler, Superprocesses and plankton dynamics, in: Monte Carlo Simulation in Oceanography, Proc. of the 'Aha Huliko'a Hawaiian Winter Workshop, Univ. of Hawai at Manoa,1997,121-128.
  • [3] H. Amann and C. Walker, Local and global strong solutions to continuous coagulation-fragmentation equations with diffusion, 3. Differential Equations 218 (2005), 159-186.
  • [4] 0. Arino and R. Rudnicki, Phytoplankton dynamics, C. R. Biologies 327 (2004), 961-969.
  • [5] J. Banasiak, On a non-uniqueness in fragmentation models. Math. Methods Appl. Sci. 25 (2002), 541-556.
  • [6] V. P. Belavkin and V. N. Kolokoltsov, On a general kinetic equation for many-particle systems with interaction, fragmentation and coagulation, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 459 (2003), 727-748.
  • [7] F. E. Boyd, M. Cai and H. Han, Rate equation and scaling for fragmentation with mass loss, Phys. Rev. A 41 (1990), 5755-5757.
  • [8] H. E. Dam and D. T. Drapeau, Coagulation efficiency, organic-matter glues and the dynamics of particle during a phytoplankton bloom in a mesocosm study, Deep-Sea Research II 42 (1995), 111-123.
  • [9] D. A. Dawson, Measure-valued Markov processes, in: Ecole d'Ete de Probabilites de Saint-Flour XXI-1991, Lecture Notes in Math. 1541, Springer, Berlin, 1993, 1-260.
  • [10] P. Donnelly and T. G. Kurtz, Particle representations for measure-valued population processes, Ann. Probab. 27 (1999), 166-205.
  • [11] R. L. Drake, A general mathematical survey of the coagulation equation, in: Topics in Current Aerosol Research (Part 2), G. M. Hidy and J. R. Brock (eds.), Pergamon Press, Oxford, 1972, 201-376.
  • [12] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1968.
  • [13] E. B. Dynkin, An Introduction to Branching Measure-Valued Processes, CRM Monogr. Ser. 6, Amer. Math. Soc., Providence, RI, 1994.
  • [14] A. Eibeck and W. Wagner, Stochastic particle approximations for Smoluchowski's coagulation equation, Ann. Appl. Probab. 11 (2001), 1137-1165.
  • [15] N. El Saadi and 0. Arino, A superprocess with spatial interactions for modelling the aggregation behavior in phytoplankton, submitted.
  • [16] A. M. Etheridge, An Introduction to Superprocesses, Univ. Lecture Ser. 20, Amer. Math. Soc., Providence, RI, 2000.
  • [17] S. N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986.
  • [18] B. Fristedt and L. Gray, A Modem Approach to Probability Theory, Birkhäuser, Boston, 1997.
  • [19] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.
  • [20] V. N. Kolokoltsov, Hydrodynamic limit of coagulation-fragmentation type models of k-nary interacting particles, 3. Statist. Phys. 115 (2004), 1621-1653.
  • [21] T. G. Kurtz, Particle representations for measure-valued population processes with spatially varying birth rates, in: Stochastic Models (Ottawa, ON, 1998), CMS Conf. Proc. 26, Amer. Math. Soc., Providence, RI, 2000, 299-317.
  • [22] P. Laurençot and S. Mischler, The continuous coagulation-fragmentation equations with diffusion. Arch. Ration. Mech. Anal. 162 (2002), 45-99.
  • [23] D. Morale, V. Capasso and K. Oelschlager, An interacting particle system modelling aggregation behavior: from individuals to populations, J. Math. Biol. 50 (2005), 49-66.
  • [24] J. R. Norris, Brownian coagulation, Comm. Math. Sci. 2 (2004), 93-101.
  • [25] —, Smoluchowski's coagulation equation: uniqueness, non-uniqueness and a hydro-dynamic limit/or the stochastic coalescent, Ann. Appl. Probab. 9 (1999) 78-109.
  • [26] U. Passow and A. L. Alldredge, Aggregation of a diatom bloom in a mesocosm: The role of transparent exopolymer particles (TEP), Deep-Sea Research II 42 (1995), 99-109.
  • [27] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, New York, 1983.
  • [28] J.-P. Roth, Operateurs elliptiques comme generateurs infinitesimaux de semi-groupes de Feller, C. R. Acad. Sci. Paris Ser. A-B 284 (1977), 755-757.
  • [29] M. von Smoluchowski, Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen, Phys. Z. 17 (1916), 557-571, 585-599.
  • [30] W. R. Young, A. J. Roberts and G. Stuhne, Reproductive pair correlations and the clustering of organisms, Nature 412 (2001), 328-331-
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0011-0027
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