Becker--Doering equations coagulation and fragmentation nonconvex Lyapunov function existence of equilibrium convergence to equilibrium On a thermodynamically consistent modification of the Becker-Doering equations Michael Herrmann Herrmann Michael Margarita Naldzhieva Naldzhieva Margarita Barbara Niethammer Niethammer Barbara Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

On a thermodynamically consistent modification of the Becker-Doering equations

Michael Herrmann , Margarita Naldzhieva, Barbara Niethammer

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

PACS: 05.45 86.03 82.60

Abstract
Recently, Dreyer and Duderstadt have proposed a modification of the Becker--Doering cluster equations which now have a nonconvex Lyapunov function. We start with existence and uniqueness results for the modified equations. Next we derive an explicit criterion for the existence of equilibrium states and solve the minimization problem for the Lyapunov function. Finally, we discuss the long time behavior in the case that equilibrium solutions do exist.

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