Chemical kinetic functional sensitivity analysis: Elementary sensitivities

Sensitivity analysis is considered for kinetics problems defined in the space–time domain. This extends an earlier temporal Green’s function method to handle calculations of elementary functional sensitivities dui/daj where ui is the ith species concentration and aj is the jth system parameter. The system parameters include rate constants, diffusion coefficients, initial conditions, boundary conditions, or any other well-defined variables in the kinetic equations. These parameters are generally considered to be functions of position and/or time. Derivation of the governing equations for the sensitivities and the Green’s funciton are presented. The physical interpretation of the Green’s function and sensitivities is given along with a discussion of the relation of this work to earlier research.