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June  2005, 4(2): 463-473. doi: 10.3934/cpaa.2005.4.463

Asymptotic behavior of solutions to the nonlinear breakage equations

Lie Zheng 1,

1. 

Department of Mathematics and Physics, Hubei University of Technology, Wuhan Hubei 430068, China

Received  April 2004 Revised  December 2004 Published  March 2005

The nonlinear breakage equations are a mathematical model for the dynamics of cluster growth when clusters undergo binary collisions resulting either in coalescence or breakup with possible transfer of matter. Each of these two events may happen with an a priori prescribed probability depending for instance on the sizes of the colliding clusters. The model consists of a countable number of non-locally coupled nonlinear ordinary differential equations modeling the concentration of the various clusters. In the present paper we consider asymptotic behavior of solutions as time tends to infinity and prove the weak* convergence to steady states provided at least two monoclusters appear after a collision, and the weak* convergence to some equilibrium state at the expense of making stronger assumptions. A result on the strong convergence has also been obtained.
Keywords: equilibria., strong convergence, Banach spaces, weak* convergence.
Mathematics Subject Classification: 34A34,82C82.
Citation: Lie Zheng. Asymptotic behavior of solutions to the nonlinear breakage equations. Communications on Pure and Applied Analysis, 2005, 4 (2) : 463-473. doi: 10.3934/cpaa.2005.4.463
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