engleski

Hilbert space approach to PDEs of Friedrichs type

The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond, and Caplain (2007), and by Antonić and Burazin (2010), while more recently a purely operator-theoretic description of abstract Friedrichs systems is developed. In this talk we shall present this abstract theory of Friedrichs systems and apply it on several boundary value problems of interest. At the end we study the question whether for any differential operator of the Friedrichs type there exist boundary conditions such that the problem is well-posed. This talk is based on joint works with Nenad Antonić, Krešimir Burazin, Ivana Crnjac, and Alessandro Michelangeli.

symmetric positive first-order system of partial differential equations ; Krein space ; universal parametrisation of extensions

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