Abstract
In this paper, we are concerned with well-posedness of an anisotropic parabolic equation with the convection term. When some diffusion coefficients are degenerate on the boundary ∂Ω and the others are positive on Ω‾, we propose a novel partial boundary value condition to study the stability of the solutions for the anisotropic parabolic equation. A new concept, the general characteristic function of the domain Ω, is introduced and applied. The existence and stability of the solutions is established under the given partial boundary value conditions.
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