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Spectral analysis of perturbed multiplication operators occurring in polymerisation chemistry

Published online by Cambridge University Press:  14 November 2011

Niels Jørgen Kokholm
Niels Jørgen Kokholm
Affiliation:
Københavns Universitets Matematiske Institut, Universitetsparken 5, DK-2100 København ø, Denmark
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Synopsis

We consider a mathematical model for the motion of a marked monomer in a system of reacting polymers at equilibrium. A well-posed integro-differential initial value problem for the probability of finding the marked monomer in a molecule of a given length is formulated. We prove exponential convergence of the probability to a unique equilibrium distribution. A quite complete spectral analysis is carried out for a self adjoint operator, which is a perturbation of a multiplication operator by an integral operator and is related to the generator of the time evolution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 113 , Issue 1-2 , 1989 , pp. 119 - 148
Copyright
Copyright © Royal Society of Edinburgh 1989

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