Friedrichs systems in a Hilbert space framework : Solvability and multiplicity (CROSBI ID 243323)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Antonić, Nenad ; Erceg, Marko ; Michelangeli, Alessandro
engleski
Friedrichs systems in a Hilbert space framework : Solvability and multiplicity
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). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide sufficient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.
Symmetric positive first-order system of partial differential equations ; Kreĭn space ; Universal parametrisation of extensions
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Podaci o izdanju
263 (12)
2017.
8264-8294
objavljeno
0022-0396
1090-2732
10.1016/j.jde.2017.08.051