Stability conditions for a class of distributed-parameter systems and their applications to chemical reaction systems

Abstract A sufficient condition for stability of a class of distributed-parameter systems is derived by use of Liapunov's direct method. This condition is not only sufficient necessary for a restricted class of systems in which the accessory boundary value problem is self-adjoint. Two applications are given in which stability conditions are derived for a tubular reactor with axial diffusion and a chemical reaction system in a catalyst particle with internal diffusion. As for the latter application, the sufficient condition obtained is probably equivalent to the condition which has been derived by Kuo and Amundson by use of the theory of eigenfunctions. It has, however, the advantage of avoiding the direct calculation of the eigenvalues of the corresponding eigenvalue problem. It only requires to solve an initial value problem of a set of linear ordinary differential equations.