AUTHORS: Huashui Zhan

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ABSTRACT: By reviewing Fichera-Oleˇinik theory, the portion of the boundary on which we should give the boundary value is determined, the corresponding initial-boundary value problem of the strongly degenerate parabolic equation ∂u ∂t = ∆A(u) + div(b(u, x, t)), (x, t) ∈ Ω × (0, T), is considered. By introducing a new kind of entropy solution, we are able to get the existence and the stability of the solutions.

KEYWORDS: Initial-boundary value problem, boundary condition, Fichera-Oleˇinik theory, entropy solution, existence, stability.;

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[28] H. Zhan, The solution of a hyperbolic-parabolic mixed-type equation on half-space domain, J. of Diff. Equ. 259, 1449-1481(2015)