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There are fruitful results on degenerate parabolic-hyperbolic equations recently following the idea of Kružkov’s doubling variables device. This paper is devoted to the well-posedness of nonhomogeneous boundary problem for degenerate parabolic-hyperbolic equations with spatially dependent second order operator, which has not caused much attention. The novelty is that we use the boundary flux triple instead of boundary layer to treat this problem.

NONHOMOGENEOUS DIRICHLET PROBLEM FOR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATIONS WITH SPATIALLY DEPENDENT SECOND ORDER OPERATOR