The Becker-Döring model with diffusion. I. Basic properties of solutions

• Autorzy: Philippe Laurençot , Dariusz Wrzosek
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 75
• Numer: 2
• Strony: 245-269

Daty

wydano

1998

otrzymano

1997-05-15

Twórcy

autor

Philippe Laurençot

• Institut Elie Cartan-Nancy, Université de Nancy I, BP 239, F-54506 Vandœuvre-lès-Nancy Cedex, France

autor

Dariusz Wrzosek

• Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

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• [8] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs 23, Amer. Math. Soc., Providence, 1968.
• [9] Ph. Laurençot and D. Wrzosek, Fragmentation-diffusion model. Existence of solutions and asymptotic behaviour, Proc. Roy. Soc. Edinburgh Sect. A, to appear.
• [10] Ph. Laurençot and D. Wrzosek, The Becker-Döring model with diffusion. II. Long time behaviour, submitted.
• [11] R. H. Martin and M. Pierre, Nonlinear reaction-diffusion systems, in: Nonlinear Equations in Applied Science, W. F. Ames and C. Rogers (eds.), Academic Press, Boston, 1992.
• [12] O. Penrose and A. Buhagiar, Kinetics of nucleation in a lattice gas model: microscopic theory and simulation compared, J. Statist. Phys. 30 (1983), 219-241.
• [13] F. Rothe, Global Solutions of Reaction-Diffusion Systems, Lecture Notes in Math. 1072, Springer, Berlin, 1984.
• [14] M. Slemrod, Trend to equilibrium in the Becker-Döring cluster equations, Nonlinearity 2 (1989), 429-443.
• [15] J. L. Spouge, An existence theorem for the discrete coagulation-fragmentation equations, Math. Proc. Cambridge Philos. Soc. 96 (1984), 351-357.
• [16] D. Wrzosek, Existence of solutions for the discrete coagulation-fragmentation model with diffusion, Topol. Methods Nonlinear Anal. 9 (1997), 279-296.
• [17] A. Ziabicki, Generalized theory of nucleation kinetics. IV. Nucleation as diffusion in the space of cluster dimensions, positions, orientations and internal structure, J. Chem. Phys. 85 (1986), 3042-3056.