Publication 19-CNA-006

Temporal oscillations in Becker-Doering equations with atomization

Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
rpego@andrew.cmu.edu

Juan J. L. Velázquez
Institut für Angewandte Mathematik
Universität Bonn
Endenicher Allee 60
53115 Bonn, Germany
velazquez@iam.uni-bonn.de

Abstract: We prove that time-periodic solutions arise via Hopf bifurcation in a finite closed system of coagulation-fragmentation equations. The system we treat is a variant of the Becker-Doering equations, in which clusters grow or shrink by addition or deletion of monomers. To this is added a linear atomization reaction for clusters of maximum size. The structure of the system is motivated by models of gas evolution oscillators in physical chemistry, which exhibit temporal oscillations under certain input/output conditions.

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