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A non-local diffusion equation arising in terminally attached polymer chains†

Published online by Cambridge University Press:  16 July 2009

Xinfu Chen  and
Avner Friedman
Xinfu Chen
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
Avner Friedman
Affiliation:
Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

We consider a polymer melt in a domain Ω whereby each polymer chain is attached at one endpoint to a fixed surface S contained in ∂Ω. Denote by G(x, t;y) the normalized number density of all subchains from x to y of length t. Then, according to the selfconsistent mean field theory, G satisfies, for each y: Gt - Δ2G + σϕG = 0, where σ is a real parameter, and ϕ is a functional of G(·, ·; ·) both non-local and nonlinear. We establish the existence of G and C∞ regularity of ϕ, as a function of x.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 4 , December 1990 , pp. 311 - 326
Copyright
Copyright © Cambridge University Press 1990

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