Standard diffusive systems are well-posed linear systems

The class of well-posed linear systems as introduced by Salamon has become a well-understood class of systems, see e.g. the work of Weiss and the book of Staffans. Many partial partial differential equations with boundary control and point observation can be formulated as a well-posed linear system. In parallel to the development of well-posed linear systems, the class of diffusive systems has been developed. This class is used to model systems for which the impulse response has a long tail, i.e., decays slowly, or systems with a diffusive nature, like the Lokshin model in acoustics. Another class of models arethe fractional differential equations, i.e., a system which has fractional powers of s in its transfer function