Marko Erceg

Complex Friedrichs systems and applications

Recently, there has been a significant development of the abstract theory of Friedrichs systems in Hilbert spaces [Ern, A., Guermond, J.-L., and Caplain, G., Commun. Partial Differ. Equations 32, 317–341 (2007) and Antonic, N. and Burazin, K., Commun. Partial Differ. Equations 35, 1690–1715 (2010)] and its applications to specific problems in mathematical physics. However, these applications were essentially restricted to real systems. We check that the already developed theory of abstract Friedrichs systems can be adjusted to the complex setting, with some necessary modifications, which allows for applications to partial differential equations with complex coefficients. We also provide examples where the involved Hilbert space is not the space of square integrable functions, as it was the case in previous studies, 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 Di...