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Fragmentation-diffusion model. Existence of solutions and their asymptotic behaviour. (English) Zbl 0912.35031
The discrete fragmentation-diffusion infinite system is studied. It describes dynamics of clusters degradation in the framework of discrete coagulation-fragmentation models. The fields of applications are polymer science, atmosphere physics and colloidal chemistry. The authors consider only mass-preserving (MPS) solutions. Existence of MPS is proved, and MPS are constructed as the limit of solutions of finite systems approximating the original one. Well-posedness for MPS is obtained. The long-time behaviour of MPS is investigated, and asymptotic convergence to spatially homogeneous equilibrium states is obtained.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
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References:
[1] Deuflhard, Computational Ordinary Differential Equations pp 287– (1992)
[2] DOI: 10.1007/BF01023480
[3] DOI: 10.1080/00411459608220717 · Zbl 0870.35117
[4] DOI: 10.1007/BF02186834 · Zbl 0838.60089
[5] Carr, Proc. Roy. Soc. Edinburgh Sect. A 121 pp 231– (1992) · Zbl 0760.34044
[6] Bénilan, Adv. Math. Sci. Appl. 7 pp 349– (1997)
[7] Baras, C. R. Acad. Sci. Paris, Sér. A 286 pp 1113– (1978)
[8] DOI: 10.1007/BF01013961 · Zbl 1217.82050
[9] DOI: 10.1007/BF02774019 · Zbl 0535.35017
[10] DOI: 10.1088/0305-4470/18/15/026
[11] DOI: 10.1007/BF01012594
[12] Smoluchowski, Z. Phys. Chem. 92 pp 129– (1917)
[13] DOI: 10.1016/0167-2789(90)90098-A · Zbl 0732.35103
[14] Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations (1983) · Zbl 0516.47023
[15] Martin, Nonlinear Equations in Applied Science (1992)
[16] DOI: 10.1007/BF01019497
[17] Drake, Topics in Current Aerosol Research pp 202– (1972)
[18] DOI: 10.1016/S0167-2789(97)00178-4 · Zbl 0960.82017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.