Parameter identification in reaction-diffusion models
Avner Friedman, Fernando L. Reitich · Inverse Problems · 1992
The authors consider certain one-dimensional reaction-diffusion models for two chemical substances with concentrations A (the reducing agent) and B (the coupler). The reducing agent diffuses and combines with the coupler. Both the diffusion coefficient D and the reaction rate k are unknown. The measurable quantity is the total concentration h(t) of the reducing agent, or its concentration g(t) at the wall of the container, at each time t. The problem is therefore to identify D and k from the knowledge of h or g. An asymptotic expansion of A for small times reveals the dependence of h(t) and g(t) on D and k thereby allowing one to identify these coefficients.