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Trend to Equilibrium for the Coagulation–Fragmentation Equation

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

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
502 KB
Volume
19
Category
Article
ISSN
0170-4214

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✦ Synopsis

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-dependent solutions with the same density can tend to only one particular steady-state solution. In this sense the equilibrium solution is proved to be unique. Existence, uniqueness and mass conservation of time-dependent solutions has been proved in a previous paper by the authors [lo].

📜 SIMILAR VOLUMES

Approach to Equilibrium for the Coagulat
Approach to Equilibrium for the Coagulation–Fragmentation Equation via a Lyapunov Functional
✍ I. W. Stewart; P. B. Dubovskiǐ 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 624 KB

## 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 t

Existence and uniqueness results for the
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✍ Wilson Lamb 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 147 KB 👁 1 views

## Abstract A non‐linear integro‐differential equation modelling coagulation and fragmentation is investigated using the theory of strongly continuous semigroups of operators. Under the assumptions that the coagulation kernel is bounded and the overall rate of fragmentation satisfies a linear growt

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Existence and uniqueness results for the non-autonomous coagulation and multiple-fragmentation equation
✍ D. J. McLaughlin; W. Lamb; A. C. McBride 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 154 KB 👁 2 views

An initial-value problem modelling coagulation and fragmentation processes is studied. The results of earlier papers are extended to models where either one or both of the rates of coagulation and fragmentation depend on time. An abstract integral equation, involving the solution operator to the lin