A non-local diffusion equation arising in terminally attached polymer chains
Xinfu Chen, Avner Friedman · European Journal of Applied Mathematics · 1990
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.