State Trajectories Analysis for a Class of Tubular Reactor Nonlinear Nonautonomous Models

Several chemical and biochemical processes are typically described by nonlinear coupled partial differential equations “PDE” and hence by distributed parameter models see 1 and the references within . The source of nonlinearities is essentially the kinetics of the reactions involved in the process. For numerical simulation as well as for control design problems, many authors approximate those distributed parameter systems by lumped parameter models 1– 5 . However, an important number of questions remained unsolved. In particular, to study the stability of the tubular reactor, the trajectory must exist on the whole real positive time interval 0, ∞ . In our previous works 6, 7 , we have proven the global state trajectories existence for a class of nonlinear systems arising from convection-dispersion-reaction systems, assuming that the inlet concentrations are independent of time. In this paper, we investigate the question in the case where the involved inlet concentrations are functions of time t. The considered class of models correspond to the following chemical reaction: