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Preface
Transport processes with coagulation and strong fragmentation
1. | School of Mathematical Sciences, University of KwaZulu-Natal, Durban |
References:
[1] |
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.
doi: 10.1007/s002850050062. |
[2] |
O. Arino and R. Rudnicki, Phytoplankton dynamics, Comptes Rendus Biologies, 327 (2004), 961-969.
doi: 10.1016/j.crvi.2004.03.013. |
[3] |
J. Banasiak and L. Arlotti, "Perturbations of Positive Semigroups with Applications," Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 2006. |
[4] |
J. Banasiak, On non-uniqueness in fragmentation models, Math. Methods Appl. Sci., 25 (2002), 541-556.
doi: 10.1002/mma.301. |
[5] |
J. Banasiak, Conservative and shattering solutions for some classes of fragmentation models, Math. Models Methods Appl. Sci., 14 (2004), 483-501.
doi: 10.1142/S0218202504003325. |
[6] |
J. Banasiak, On conservativity and shattering for an equation of phytoplankton dynamics, Comptes Rendus Biologies, 337 (2004), 1025-1036.
doi: 10.1016/j.crvi.2004.07.017. |
[7] |
J. Banasiak, Shattering and non-uniqueness in fragmentation models--an analytic approach, Physica D, 222 (2006), 63-72.
doi: 10.1016/j.physd.2006.07.025. |
[8] |
J. Banasiak and W. Lamb, On a coagulation and fragmentation equation with mass loss, Proc. Roy. Soc. Edinburgh Sec. A, 136 (2006), 1157-1173.
doi: 10.1017/S0308210500004923. |
[9] |
J. Banasiak and W. Lamb, Coagulation, fragmentation and growth processes in a size structured population, Discrete Contin. Dyn. Sys. Ser. B, 11 (2009), 563-585.
doi: 10.3934/dcdsb.2009.11.563. |
[10] |
J. Banasiak and M. Mokhtar-Kharroubi, Universality of dishonesty of substochastic semigroups: Shattering fragmentation and explosive birth-and-death processes, Discrete Contin. Dyn. Sys. B, 5 (2005), 524-542. |
[11] |
J. Banasiak, S. C. Oukoumi Noutchie and R. Rudnicki, Global solvability of a fragmentation-coagulation eqation with growth and restricted coagulation, J. Nonlinear Math. Phys., 16 (2009), 13-26.
doi: 10.1142/S1402925109000297. |
[12] |
J. Banasiak and W. Lamb, Global strict solutions to continuous coagulation-fragmentation equations with strong fragmentation, Proc. Roy. Soc. Edinburgh Sec. A, 141 (2011), 465-480.
doi: 10.1017/S0308210509001255. |
[13] |
M. Cai, B. F. Edwards and H. Han, Exact and asymptotic scaling solutions for fragmentation with mass loss, Phys. Rev. A (3), 43 (1991), 656-662.
doi: 10.1103/PhysRevA.43.656. |
[14] |
J. Carr and F. P. da Costa, Asymptotic behavior of solutions to the coagulation-fragmentation equations. II. Weak fragmentation, J. Stat. Phys., 77 (1994), 89-123.
doi: 10.1007/BF02186834. |
[15] |
B. F. Edwards, M. Cai and H. Han, Rate equation and scaling for fragmentation with mass loss, Phys. Rev. A, 41 (1990), 5755-5757.
doi: 10.1103/PhysRevA.41.5755. |
[16] |
M. Escobedo, Ph. Laurençot, S. Mischler and B. Perthame, Gelation and mass conservation in coagulation-fragmentation models, J. Differential Equations, 195 (2003), 143-174.
doi: 10.1016/S0022-0396(03)00134-7. |
[17] |
B. Haas, Loss of mass in deterministic and random fragmentations, Stochastic Process. Appl., 106 (2003), 245-277.
doi: 10.1016/S0304-4149(03)00045-0. |
[18] |
J. Huang, B. E. Edwards and A. D. Levine, General solutions and scaling violation for fragmentation with mass loss, J. Phys. A: Math. Gen., 24 (1991), 3967-3977.
doi: 10.1088/0305-4470/24/16/031. |
[19] |
J. Huang, X. P. Guo, B. F. Edwards and A. D. Levine, Cut-off model and exact general solutions for fragmentation with mass loss, J. Phys. A: Math. Gen., 29 (1996), 7377-7388.
doi: 10.1088/0305-4470/29/23/008. |
[20] |
G. A. Jackson, A model of formation of marine algal flocks by physical coagulation processes, Deep-Sea Research, 37 (1990), 1197-1211.
doi: 10.1016/0198-0149(90)90038-W. |
[21] |
M. Kostoglou and A. J. Karabelas, On the breakage problem with a homogeneous erosion type kernel, J. Phys. A, 34 (2001), 1725-1740.
doi: 10.1088/0305-4470/34/8/316. |
[22] |
P. Laurençot, On a class of continuous coagulation-fragmentation equations, J. Differential Equations, 167 (2000), 245-274.
doi: 10.1006/jdeq.2000.3809. |
[23] |
E. D. McGrady and R. M. Ziff, "Shattering'' transition in fragmentation, Phys. Rev. Lett., 58 (1987), 892-895.
doi: 10.1103/PhysRevLett.58.892. |
[24] |
A. Okubo and S. A. Levin, "Diffusion and Ecological Problems: Modern Perspectives," Second edition, Interdisciplinary Applied Mathematics, 14, Springer-Verlag, New York, 2001. |
[25] |
B. Perthame, "Transport Equations in Biology," Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2007. |
[26] |
J. Prüss, L. Pujo-Menjouet, G. F. Webb and R. Zacher, Analysis of a model for the dynamics of prions, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 225-235. |
[27] |
R. Rudnicki and R. Wieczorek, Phytoplankton dynamics: From the behaviour of cells to a transport equation, Math. Model. Nat. Phenom., 1 (2006), 83-100.
doi: 10.1051/mmnp:2006005. |
[28] |
R. M. Ziff and E. D. McGrady, The kinetics of cluster fragmentation and depolymerization, J. Phys. A, 18 (1985), 3027-3037.
doi: 10.1088/0305-4470/18/15/026. |
[29] |
R. M. Ziff and E. D. McGrady, Kinetics of polymer degradation, Macromolecules, 19 (1986), 2513-2519.
doi: 10.1021/ma00164a010. |
show all references
References:
[1] |
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.
doi: 10.1007/s002850050062. |
[2] |
O. Arino and R. Rudnicki, Phytoplankton dynamics, Comptes Rendus Biologies, 327 (2004), 961-969.
doi: 10.1016/j.crvi.2004.03.013. |
[3] |
J. Banasiak and L. Arlotti, "Perturbations of Positive Semigroups with Applications," Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 2006. |
[4] |
J. Banasiak, On non-uniqueness in fragmentation models, Math. Methods Appl. Sci., 25 (2002), 541-556.
doi: 10.1002/mma.301. |
[5] |
J. Banasiak, Conservative and shattering solutions for some classes of fragmentation models, Math. Models Methods Appl. Sci., 14 (2004), 483-501.
doi: 10.1142/S0218202504003325. |
[6] |
J. Banasiak, On conservativity and shattering for an equation of phytoplankton dynamics, Comptes Rendus Biologies, 337 (2004), 1025-1036.
doi: 10.1016/j.crvi.2004.07.017. |
[7] |
J. Banasiak, Shattering and non-uniqueness in fragmentation models--an analytic approach, Physica D, 222 (2006), 63-72.
doi: 10.1016/j.physd.2006.07.025. |
[8] |
J. Banasiak and W. Lamb, On a coagulation and fragmentation equation with mass loss, Proc. Roy. Soc. Edinburgh Sec. A, 136 (2006), 1157-1173.
doi: 10.1017/S0308210500004923. |
[9] |
J. Banasiak and W. Lamb, Coagulation, fragmentation and growth processes in a size structured population, Discrete Contin. Dyn. Sys. Ser. B, 11 (2009), 563-585.
doi: 10.3934/dcdsb.2009.11.563. |
[10] |
J. Banasiak and M. Mokhtar-Kharroubi, Universality of dishonesty of substochastic semigroups: Shattering fragmentation and explosive birth-and-death processes, Discrete Contin. Dyn. Sys. B, 5 (2005), 524-542. |
[11] |
J. Banasiak, S. C. Oukoumi Noutchie and R. Rudnicki, Global solvability of a fragmentation-coagulation eqation with growth and restricted coagulation, J. Nonlinear Math. Phys., 16 (2009), 13-26.
doi: 10.1142/S1402925109000297. |
[12] |
J. Banasiak and W. Lamb, Global strict solutions to continuous coagulation-fragmentation equations with strong fragmentation, Proc. Roy. Soc. Edinburgh Sec. A, 141 (2011), 465-480.
doi: 10.1017/S0308210509001255. |
[13] |
M. Cai, B. F. Edwards and H. Han, Exact and asymptotic scaling solutions for fragmentation with mass loss, Phys. Rev. A (3), 43 (1991), 656-662.
doi: 10.1103/PhysRevA.43.656. |
[14] |
J. Carr and F. P. da Costa, Asymptotic behavior of solutions to the coagulation-fragmentation equations. II. Weak fragmentation, J. Stat. Phys., 77 (1994), 89-123.
doi: 10.1007/BF02186834. |
[15] |
B. F. Edwards, M. Cai and H. Han, Rate equation and scaling for fragmentation with mass loss, Phys. Rev. A, 41 (1990), 5755-5757.
doi: 10.1103/PhysRevA.41.5755. |
[16] |
M. Escobedo, Ph. Laurençot, S. Mischler and B. Perthame, Gelation and mass conservation in coagulation-fragmentation models, J. Differential Equations, 195 (2003), 143-174.
doi: 10.1016/S0022-0396(03)00134-7. |
[17] |
B. Haas, Loss of mass in deterministic and random fragmentations, Stochastic Process. Appl., 106 (2003), 245-277.
doi: 10.1016/S0304-4149(03)00045-0. |
[18] |
J. Huang, B. E. Edwards and A. D. Levine, General solutions and scaling violation for fragmentation with mass loss, J. Phys. A: Math. Gen., 24 (1991), 3967-3977.
doi: 10.1088/0305-4470/24/16/031. |
[19] |
J. Huang, X. P. Guo, B. F. Edwards and A. D. Levine, Cut-off model and exact general solutions for fragmentation with mass loss, J. Phys. A: Math. Gen., 29 (1996), 7377-7388.
doi: 10.1088/0305-4470/29/23/008. |
[20] |
G. A. Jackson, A model of formation of marine algal flocks by physical coagulation processes, Deep-Sea Research, 37 (1990), 1197-1211.
doi: 10.1016/0198-0149(90)90038-W. |
[21] |
M. Kostoglou and A. J. Karabelas, On the breakage problem with a homogeneous erosion type kernel, J. Phys. A, 34 (2001), 1725-1740.
doi: 10.1088/0305-4470/34/8/316. |
[22] |
P. Laurençot, On a class of continuous coagulation-fragmentation equations, J. Differential Equations, 167 (2000), 245-274.
doi: 10.1006/jdeq.2000.3809. |
[23] |
E. D. McGrady and R. M. Ziff, "Shattering'' transition in fragmentation, Phys. Rev. Lett., 58 (1987), 892-895.
doi: 10.1103/PhysRevLett.58.892. |
[24] |
A. Okubo and S. A. Levin, "Diffusion and Ecological Problems: Modern Perspectives," Second edition, Interdisciplinary Applied Mathematics, 14, Springer-Verlag, New York, 2001. |
[25] |
B. Perthame, "Transport Equations in Biology," Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2007. |
[26] |
J. Prüss, L. Pujo-Menjouet, G. F. Webb and R. Zacher, Analysis of a model for the dynamics of prions, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 225-235. |
[27] |
R. Rudnicki and R. Wieczorek, Phytoplankton dynamics: From the behaviour of cells to a transport equation, Math. Model. Nat. Phenom., 1 (2006), 83-100.
doi: 10.1051/mmnp:2006005. |
[28] |
R. M. Ziff and E. D. McGrady, The kinetics of cluster fragmentation and depolymerization, J. Phys. A, 18 (1985), 3027-3037.
doi: 10.1088/0305-4470/18/15/026. |
[29] |
R. M. Ziff and E. D. McGrady, Kinetics of polymer degradation, Macromolecules, 19 (1986), 2513-2519.
doi: 10.1021/ma00164a010. |
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