| Abstract: |
| In this talk, we consider Cauchy problems of linear and semilinear polyharmonic heat equations. It is known that Cauchy problems of higher order parabolic equations have no positivity preserving property in general. On the other hand, it is expected that solutions to Cauchy problems of polyharmonic heat equations are eventually globally positive if initial data decay slowly enough.
Our aim of this talk is to show the existence of the threshold for the decay rate of initial data which determines whether the corresponding solution to the Cauchy problem of the linear polyharmonic heat equation is eventually globally positive or not. As the application of this result, we construct eventually globally positive solutions to a Cauchy problem of a semilinear polyharmonic heat equation. |
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