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Classical solutions of mixed problems for quasilinear first order PFDEs on a cylindrical domain
We abandon the setting of the domain as a Cartesian product of real intervals, customary for first order PFDEs (partial functional differential equations) with initial boundary conditions. We give a new set of conditions on the possibly unbounded domain Ω with Lipschitz differentiable boundary. Well-posedness is then reliant on a variant of the normal vector condition. There is a neighbourhood of ∂Ω with the property that if a characteristic trajectory has a point therein, then its everydoi:10.7494/opmath.2014.34.2.291 fatcat:nptx32vekngyblvznaicllu3xq