Boundary behavior and asymptotic behavior of solutionsto a class of parabolic equations with boundary degeneracy

Chunpeng Wang

doi:10.3934/dcds.2016.36.1041

Article Contents

2016, Volume 36, Issue 2: 1041-1060. Doi: 10.3934/dcds.2016.36.1041

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Boundary behavior and asymptotic behavior of solutions to a class of parabolic equations with boundary degeneracy

Chunpeng Wang^1,

1.
School of Mathematics, Jilin University, Changchun 130012

Received: May 31, 2014

Revised: December 31, 2014

Published: May 2017

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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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Mathematics Subject Classification: 35K65, 35D30, 35B40.

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