Arbitrary order functional sensitivity densities for reaction-diffusion systems

The concept of functional sensitivity analysis in the study of diffusion processes in a chemically reacting environment is reviewed and extended to include the notion of arbitrary order functional sensitivity densities. A new perspective on its physical and mathematical basis is offered through a detailed discussion of the motivation behind the formal procedure adopted. The arbitrary order functional sensitivity densities (defined as arbitrary order functional derivatives of a chemical species concentration with respect to the space and time dependent parameters of the system) are shown to obey certain differential equations that can be solved with the help of a Green's function. This Green's function is the inverse of a differential operator that defines an associated linear system in the application of Lyapounov's linearized stability theory to (in general nonlinear) reaction-diffusion systems. It is found that the Green's function can be regarded as a concentration response function which allows for an interpretation of the sensitivity densities as generalized response functions. Finally, an illustration of the use of those techniques is provided by applying them to the case of a linear reaction-diffusion system.