Observability estimates for convection dominated tubular reactors governed by the convection-(diffusion)-reaction pde

This paper investigates the state estimation problem for systems described by the convection-diffusion-reaction partial differential equation, with or without the diffusion term.The analysis of the observability leads to different results for the observability of the system e.g. a time-dependent approximate observability for the convection-reaction equation, this behavior does not occur for the convection-diffusion-reaction equation. To analyze these differences, a quantitative indicator of the unobservability is proposed based on the criterion of exact final observability. For the convection-reaction equation the indicator can be calculated analytically while for the convection-diffusion-reaction equation a numerical lower bound can be calculated using arbitrary precision calculation. For this indicator, the same qualitative behaviour as for the observability of the convection-reaction equation can be observed for the convection dominated convection-diffusion-reaction equation.