FWF - Friedrich - Spectral analysis of Friedrichs systems

Friedrichs introduced the concept of Friedrichs systems. It is a clever way of representing the (semi)linear partial differential equations as first-order systems. The main motivation was to treat the equations that change their type, like the Tricomi equation (which appears in the transonic flow). Moreover, it allows for a unified treatment of a wide variety of elliptic, parabolic, hyperbolic, and mixed-type equations. On the other hand, the theory of abstract Friedrichs operators was introduced in 2007, which is formulated in terms of Hilbert space theory, which avails the access of operator-theoretic results and techniques. Here the abstract notion of boundary triples and Weyl functions, which is an efficient modern tool in extension theory and spectral analysis of symmetric and self-adjoint operators allows not only a classification of all proper boundary conditions, but can also be applied to investigate various coupling problems.