01282nas a2200133 4500008004100000245004800041210004800089520088200137100002001019700002301039700001801062700001701080856005101097 2017 en d00aComplex Friedrichs systems and applications0 aComplex Friedrichs systems and applications3 aWe provide a suitable extension of the theory of abstract Friedrichs systems from
real Hilbert spaces to the complex Hilbert space setting, which allows for applications
to partial differential equations with complex coeffcients. We also provide examples
where the involved Hilbert space is not the space of square integrable functions, as it
was the case in previous works, but rather its closed subspace or the space Hs(Rd;Cr),
for real s. This setting appears to be suitable for particular systems of partial differential
equations, such as the Dirac system, the Dirac-Klein-Gordon system, the Dirac-Maxwell
system, and the time-harmonic Maxwell system, which are all addressed in the paper.
Moreover, for the time-harmonic Maxwell system we also applied a suitable version of
the two-field theory with partial coercivity assumption which is developed in the paper.1 aAntonić, Nenad1 aBurazin, Krešimir1 aCrnjac, Ivana1 aErceg, Marko uhttp://urania.sissa.it/xmlui/handle/1963/3527001281nas a2200121 4500008004100000245008200041210006900123520085300192100002001045700001701065700002901082856004801111 2017 en d00aFriedrichs systems in a Hilbert space framework: solvability and multiplicity0 aFriedrichs systems in a Hilbert space framework solvability and 3 aThe 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 suffcient 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.1 aAntonić, Nenad1 aErceg, Marko1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/35280