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Existence of solutions to coagulation-fragmentation systems with diffusion. (English) Zbl 0870.35117
Summary: We show existence of solutions to an infinite system of parabolic equations obtained by adding spatial diffusion to the classical coagulation-fragmentation equations. In the case where the spatial diffusion coefficients depend on the cluster size, local existence is shown. A global solution is obtained in the case where all the diffusivities are equal. As done in previous studies on the coagulation-fragmentation system, the method of proof relies on the truncation of the infinite system; essential in the derivative of the necessary estimates is the fact that the total concentration of particles satisfies a parabolic equation, to which the maximum principle can be applied.

35R15 PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)
35K57 Reaction-diffusion equations
82D60 Statistical mechanics of polymers
Full Text: DOI
[1] DOI: 10.1007/BF01197880 · Zbl 0458.76062
[2] DOI: 10.1007/BF01013961 · Zbl 1217.82050
[3] DOI: 10.1007/BF01211070 · Zbl 0594.58063
[4] DOI: 10.1103/PhysRevB.15.4425
[5] DOI: 10.1007/BF01023480
[6] DOI: 10.1007/BF01020286
[7] Drake R., Topics in current aerosol research volume 2 of Intern (1972)
[8] DOI: 10.1088/0305-4470/16/12/032
[9] DOI: 10.1088/0305-4470/14/12/030 · Zbl 0481.92020
[10] DOI: 10.1088/0305-4470/15/6/033
[11] Slemrod M., Physica D
[12] DOI: 10.1017/S0305004100062253 · Zbl 0541.92029
[13] White W. H., Proc. Amer. Math. Soc. 80 pp 273– (1980)
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