Bulletin of the
Korean Mathematical Society BKMS

There are fruitful results on degenerate parabolic-hyperbolic equations recently following the idea of Kru\v{z}kov'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.

Keywords: degenerate parabolic-hyperbolic equation, variable coefficients, boundary condition, entropy process solution, uniqueness

MSC numbers: 35B30, 35M12, 35K65