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Approach to Equilibrium for the Coagulation–Fragmentation Equation via a Lyapunov Functional

✍ Scribed by I. W. Stewart; P. B. Dubovskiǐ

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 624 KB
Volume: 19
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(199602)19:3<171::aid-mma765>3.0.co;2-7

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✦ Synopsis

Communicated by E. Meister

It is shown that the non-linear coagulation-fragmentation equation with constant kernels has a unique equilibrium solution. This equilibrium solution is given explicitly in terms of the initial data and the kernels. Weak L' convergence of time-dependent solutions to the unique equilibrium is demonstrated via an invariance principle employing a suitable lower semicontinuous Lyapunov functional.

📜 SIMILAR VOLUMES

Trend to Equilibrium for the Coagulation

Trend to Equilibrium for the Coagulation–Fragmentation Equation

✍ P. B. Dubovskiǐ; I. W. Stewart 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 502 KB

For a linear coagulation kernel and a constant fragmentation kernel we prove the existence of equilibrium solutions and examine asymptotic properties for time-dependent solutions which are proved to converge to the equilibria. The rate of the convergence is estimated. It is shown also that all time-