Abstract
This paper concerns the boundary behavior and the asymptotic behavior of solutions to a class of boundary-initial parabolic problems with boundary degeneracy. At the degenerate boundary, it is shown that the diffusion vanishes and the solution possesses the invariability if the degeneracy is sufficiently strong. As to the asymptotic behavior, it is proved that the decay rate is an exponential function if the degeneracy is weak enough, while a power function if it is not.
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