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Jul 31, 2015 at 12:03 comment added Peter @IgorKhavkine Thanks for your hint!
Jul 31, 2015 at 10:23 comment added Igor Khavkine Also, here's a paper that discusses such systems that are of elliptic type: Hile & Protter, Properties of overdetermined first order elliptic systems (1977).
Jul 31, 2015 at 10:19 comment added Igor Khavkine A fairly well studied class of systems that fit your criteria are "symmetric hyperbolic" equations, which is a useful search term.
Jul 31, 2015 at 9:21 history asked Peter CC BY-SA 3.0