A lyapunov function for some naturally-occurring linear homogeneous time-dependent equations

A Lyapunov function is developed for certain linear homogeneous time-dependent systems. It applies to some naturally-occurring equations of the diffusion type and is applied by way of example to xenon poisoning in a nuclear reactor and to the transient behaviour of a heat exchanger. The results have a close relation to a Lyapunov function developed earlier for certain non-linear autonomous systems. This connection is shown to hold generally.