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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.
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참고문헌 (25)
참고문헌 신청
K. Ammar / 2010 / Degenerate triply nonlinear problems with nonhomogeneous boundary con-ditions / Cent. Eur. J. Math 8(3):548~568
B. Andreianov / 2010 / Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations / J. Hyperbolic Differ. Equ 7(1):1~67
B. Andreianov / 2009 / Well-posedness results for triply nonlinear degenerate parabolic equations / J. Differential Equations 247(1):277~302
C. Bardos / 1979 / First order quasilinear equations with boundary conditions / Comm. Partial Differential Equations 4(9):1017~1034
M. Bendahmane / 2005 / Uniqueness of entropy solutions for doubly nonlin-ear anisotropic degenerate parabolic equations, Nonlinear partial differential equations and related analysis / Amer. Math. Soc. :1~27
B. Andreianov / 2010 / Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations / J. Hyperbolic Differ. Equ 7(1):1~67
B. Andreianov / 2009 / Well-posedness results for triply nonlinear degenerate parabolic equations / J. Differential Equations 247(1):277~302
C. Bardos / 1979 / First order quasilinear equations with boundary conditions / Comm. Partial Differential Equations 4(9):1017~1034
M. Bendahmane / 2005 / Uniqueness of entropy solutions for doubly nonlin-ear anisotropic degenerate parabolic equations, Nonlinear partial differential equations and related analysis / Amer. Math. Soc. :1~27
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