Friedrichs systems in a Hilbert space framework: solvability and multiplicity (CROSBI ID 653500)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | 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. This is a joint work with Nenad Antonić and Alessandro Michelangeli.
Symmetric positive first-order system of partial differential equations ; Kreĭn space ; Universal parametrisation of extensions
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Podaci o prilogu
1-1.
2017.
objavljeno
Podaci o matičnoj publikaciji
Podaci o skupu
The Fifth Najman Conference on Spectral Theory and Differential Equations
predavanje
10.09.2017-15.09.2017
Opatija, Hrvatska