Am. Brodsky et Wp. Reinhardt, EXACT SOLUTION OF THE REACTION-DIFFUSION PROBLEM FOR A PARTICLE GENERATING BAND ON A SURFACE BY RIEMANN-HILBERT MATCHING, Journal of physics. A, mathematical and general, 28(12), 1995, pp. 3453-3467
The existence of a class of exact solutions for diffusion-reaction pro
blems is demonstrated for the example of a band. The method may be app
lied to any particle source which can be analytically mapped to a band
(or a disc) situated on an infinite plane. A simple asymptotic expres
sion for the experimentally measurable collector efficiency (current-c
urrent response function) has been found.