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We present a simple and natural set of assumptions on the functions $\\psi,\\varphi$, under which: 1) these equations fall in the framework provided by \\cite{ACMEllipticFLDE, ACMMRelat} and hence they are well posed, 2) we can ensure finite propagation speed for these models, 3) a Rankine--Hugoniot analysis on traveling fronts is also performed. 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