The Redner-Ben-Avraham-Kahng coagulation system with constant coefficients: the finite-dimensional case. (English) Zbl 1327.34095
Consider the \(N\)-dimensional system
\[
{dc_j\over dt}= \sum^{N-j}_{k=1} c_{j+k} c_k- c_j \sum^N_{k=1} c_k,\quad 1\leq j\leq N,\tag{*}
\]
which represents a simplified coagulation model. The authors study the longtime behavior of the solution of the Cauchy problem to (*) with nonnegative initial conditions.
Reviewer: Klaus R. Schneider (Berlin)
MSC:
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
| 82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
References:
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| [2] | da Costa F.P., Pinto J.T., Sasportes R.: The Redner-Ben-Avraham-Kahng cluster system. São Paulo J. Math. Sci. 6(2), 171-201 (2012) · Zbl 1300.34122 · doi:10.11606/issn.2316-9028.v6i2p171-201 |
| [3] | Ispolatov I., Krapivsky P.L., Redner S.: War: the dynamics of vicious civilizations. Phys. Rev. E 54, 1274-1289 (1996) · doi:10.1103/PhysRevE.54.1274 |
| [4] | Redner S., Ben-Avraham D., Kahng B.: Kinetics of ‘cluster eating’. J. Phys. A Math. Gen. 20, 1231-1238 (1987) · doi:10.1088/0305-4470/20/5/031 |
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