Boundary behavior and asymptotic behavior of solutionsto a class of parabolic equations with boundary degeneracy
Chunpeng Wang · Discrete and Continuous Dynamical Systems · 2015
This paper concerns the boundary behavior and the asymptotic behaviorof solutions to a class of boundary-initial parabolic problems with boundary degeneracy.At the degenerate boundary, it is shown thatthe diffusion vanishes and the solution possesses the invariabilityif the degeneracy is sufficiently strong.As to the asymptotic behavior, it is proved thatthe decay rate is an exponential function if the degeneracy is weak enough,while a power function if it is not.