- Needham, D.J. and King, A.C. and Merkin, J.H., Reaction-diffusion model for autocatalytic polymerization: II. The initial value problem,
IMA Journal of Applied Mathematics (Institute of Mathematics & Its Applications), vol. 56 no. 1
pp. 65 - 86 .
(last updated on 2007/04/06)
An initial-boundary value problem arising from a simple model for radical chain polymerization is discussed in detail. General properties of the solution are derived first and it is shown that a moving interface develops. This separates a region where the polymer is sufficiently concentrated for it to be immobile from one where it is still free to diffuse. An asymptotic analysis is performed in this latter region, where it is shown that a permanent-form travelling wave (treated in Part I) develops in the long time structure and that this wave travels with its minimum possible speed. Numerical results for the full initial-boundary value problem are presented which confirm the asymptotic theory and give results in regions not accessible to this analysis.
Mathematical models;Diffusion in solids;Catalysis;Polymerization;Interfaces (materials);Numerical analysis;Asymptotic stability;Catalysts;