Abstract
A number of physical problems is described by a system of first order hyperbolic equations in a subregion of the physical domain, and of parabolic equations in the complementary domain. To state these problems correctly an investigation of the existence of the trace for a function which possesses a weak derivative in some direction is needed. This problem is solved in the paper. Also we formulate the problem for hyperbolic-parabolic equations (including the description of the transmission condition on the internal boundary), then we prove its solvability.
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