Local and global strong solutions to continuous coagulation-fragmentation equations with diffusion

Journal of Differential Equations

Volumn 218, Issue 1, 2005, Pages 159-186

  Amann, Herbert ^a   Walker, Christoph ^b  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

Coagulation; Diffusion; Fragmentation; Semigroup theory; Volume scattering

Indexed keywords

EID: 27144523168     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.09.004     Document Type: Article

References (28)

1. D.J. Aldous Deterministic and stochastic models for coalescence (aggregation coagulation): A review of the mean-field theory for probabilists Bernoulli 5 1999 3-48
2. H. Amann Dual semigroups and second order linear elliptic boundary value problems Israel J. Math. 45 1983 225-254
3. H. Amann, Linear and Quasilinear Parabolic Problems, vol. I: Abstract Linear Theory, Birkhäuser, Basel, Boston, Berlin, 1995.
4. H. Amann Coagulation-fragmentation processes Arch. Rat. Mech. Anal. 151 2000 339-366
5. H. Amann F. Weber On a quasilinear coagulation-fragmentation model with diffusion Adv. Math. Sci. Appl. 11 2001 227-263
6. I. Borsi Dynamics of liquid-liquid dispersions with unbounded fragmentation kernel Adv. Math. Sci. Appl. 11 2 2001 571-591
7. Z. Cheng S. Redner Kinetics of fragmentation J. Phys. A: Math. Gen. 23 1990 1233-1258
8. M. Deaconu N. Fournier Probabilistic approach of some discrete and continuous coagulation equations with diffusion Stochastic Proc. Appl. 101 2002 83-111
9. R.L. Drake A general mathematical survey of the coagulation equation in: G.M. Hidy J.R. Brock (Eds.) Topics in Current Aerosol Research, Part 2 1972 Pergamon Press Oxford 202-376
10. A. Fasano The dynamics of two-phase liquid dispersions: Necessity of a new approach Milan J. Math. 70 2002 245-264
11. A. Fasano F. Rosso A new model for the dynamics of dispersions in a batch reactor: Theory and numerical simulations in: H.J. Bungartz R.H.W. Hoppe C. Zenger (Eds.) Proceedings of the Symposium Organized by the Sonderforschungsbereich 438 on the Occasion of Karl-Heinz Hoffman's 60th Birthday Berlin 2000 123-141
12. A. Friedman Partial Differential Equations 1969 Holt, Rinehart and Winston New York
13. T. Kato Perturbation Theory for Linear Operators 1966 Springer New York
14. P. Laurençot S. Mischler The continuous coagulation-fragmentation equations with diffusion Arch. Rat. Mech. Anal. 162 1 2002 45-99
15. P. Laurençot S. Mischler On coalescence equations and related models in: P. Degond L. Pareschi G. Russo (Eds.) Modeling and Computational Methods for Kinetic Equations 2004 Birkhäuser Boston
16. P. Laurençot D. Wrzosek The discrete coagulation equations with collisional breakage J. Statist. Phys. 104 1-2 2001 193-253
17. A. Mancini F. Rosso A new model for the dynamics of dispersions in a batch reactor: Numerical approach Meccanica 37 3 2002 221-237
18. S. Mischler M. Rodriguez-Ricard Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions C. R. Acad. Sci. Paris Sér. I Math. 336 2003 407-412
19. A. Pazy Semigroups of Linear Operators and Applications to Partial Differential Equations 1983 Springer Berlin, Heidelberg, New York
20. F. Rothe Global Solutions of Reaction-Diffusion Systems Lecture Notes in Mathematics vol. 1072 1984 Springer Berlin, Heidelberg, New York, Tokyo
21. T. Runst W. Sickel Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations De Gruyter Series in Nonlinear Analysis and Applications vol. 3 1996 De Gruyter Berlin, New York
22. p with boundary conditions Studia Math. 44 1972 47-60
23. H. Triebel Interpolation Theory, Function Spaces, Differential Operators second ed. 1995 Johann Ambrosius Barth Heidelberg, Leipzig
24. C. Walker Coalescence and breakage processes Math. Methods Appl. Sci. 25 2002 729-748
25. C. Walker Asymptotic behaviour of liquid-liquid dispersions Proc. Roy. Soc. Edinburgh Section A 134 4 2004 753-772
26. C. Walker The discrete diffusive coagulation-fragmentation equations with scattering Nonlinear Anal. 58 1-2 2004 121-142
27. C. Walker, On a new model for continuous coalescence and breakage processes with diffusion, Adv. Differential Equations, to appear.
28. D. Wrzosek Mass-conserving solutions to the discrete coagulation-fragmentation model with diffusion Nonlinear Anal. 49 2002 297-314