On the Oort-Hulst-Safronov coagulation equation and its relation to the Smoluchowski equation

SIAM Journal on Mathematical Analysis

Volumn 34, Issue 6, 2003, Pages 1399-1421

  Lachowicz, Mirosław ^a   Laurençot, Philippe ^b   Wrzosek, Dariusz ^a  

^a UNIVERSITY OF WARSAW   (Poland)

^b CNRS   (France)

Author keywords

Coagulation; Existence; Finite speed of propagation; Gelation; Oort Hulst Safronov equation; Smoluchowski equation

Indexed keywords

EID: 0242511215     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141002414470     Document Type: Article

References (21)

1. N. BELLOMO AND M. LO SCHIAVO, Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models, World Scientific, River Edge, NJ, 2000.
2. F. P. DA COSTA, On the positivity of solutions to the Smoluchowski equations, Mathematika, 42 (1995), pp. 406-412.
3. S. CHANDRASEKHAR, Stochastic problems in physics and astronomy, Rev. Modern Phys., 15 (1943), pp. 1-91.
4. C. DELLACHERIE AND P. A. MEYER, Probabilités et Potentiel, Chapitres I à IV, Hermann, Paris, 1975.
5. P. G. J. VAN DONGEN AND M. H. ERNST, Scaling solutions of Smoluchowski's coagulation equation, J. Statist. Phys., 50 (1988), pp. 295-329.
6. R. L. DRAKE, A general mathematical survey of the coagulation equation, in Topics in Current Aerosol Research, Part 2, International Reviews in Aerosol Physics and Chemistry, Pergamon Press, Oxford, UK, 1972, pp. 203-376.
7. P. B. DUBOVSKI, A "triangle" of interconnected coagulation models, J. Phys. A, 32 (1999), pp. 781-793.
8. P. B. DUBOVSKI, A new discrete model of coagulation kinetics and the properties of its continuous analogue, Mat. Model., 12 (2000), pp. 4-15 (in Russian).
9. M. ESCOBEDO, S. MISCHLER, AND B. PERTHAME, Gelation in coagulation and fragmentation models, Comm. Math. Phys., 231 (2002), pp. 157-188.
10. I. JEON, Existence of gelling solutions for coagulation-fragmentation equations, Comm. Math. Phys., 194 (1998), pp. 541-567.
11. M. LACHOWICZ AND D. WRZOSEK, Nonlocal bilinear equations. Equilibrium solutions and diffusive limit, Math. Models Methods Appl. Sci., 11 (2001), pp. 1393-1409.
12. PH. LAURENÇOT, The Lifshitz-Slyozov equation with encounters, Math. Models Methods Appl. Sci., 11 (2001), pp. 731-748.
13. PH. LAURENÇOT AND S. MISCHLER, From the discrete to the continuous coagulation-fragmentation equations, Proc. Roy. Soc. Edinburgh Sect. A, 132 (2002), pp. 1219-1248.
14. ̀me cycle, Université de Paris VI, 1977.
15. J. H. OORT AND H. C. VAN DE HULST, Gas and smoke in interstellar space, Bull. Astron. Inst. Netherland, 10 (1946), pp. 187-210.
16. A. S. PERELSON AND R. W. SAMSEL, Kinetics of red blood cell aggregation: An example of geometric polymerization, in Kinetics of Aggregation and Gelation, F. Family and D. P. Landau, eds., Elsevier, Amsterdam, 1984, pp. 137-144.
17. V. S. SAFRONOV, Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets, Israel Program for Scientific Translations, Jerusalem, 1972.
18. M. SMOLUCHOWSKI, Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen, Physik. Zeitschr., 17 (1916), pp. 557-599.
19. M. SMOLUCHOWSKI, Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen, Zeitschrift f. physik. Chemie, 92 (1917), pp. 129-168.
20. I. W. STEWART, A global existence theorem for the general coagulation-fragmentation equation with unbounded kernels, Math. Methods Appl. Sci., 11 (1989), pp. 627-648.
21. I. I. VRABIE, Compactness Methods for Nonlinear Evolutions, 2nd ed., Pitman Monogr. Surveys Pure Appl. Math. 75, Longman Scientific and Technical, Harlow, UK, 1995.