Exponential Stability of a Class of Hyperbolic PDE Models from Chemical Engineering

We study a class of dynamical systems described by symmetric hyperbolic partial differential equations (abbreviated to PDE). We prove some exponential stability result for this class of systems by constructing Lyapunov functionals. Moreover we apply this classical result for a chemical engineering system - heat exchangers to prove its exponential stability. Through concrete example we show how the Lyapunov direct method may be extended to study stability of hyperbolic PDE systems. We apply the method of finite differences to semi-discretize and to solve numerically the heat exchanger system. In conformity with what is expected, the numerical result shows the asymptotic stability of the heat exchanger process