On the asymptotic behaviour of the pure Neumann problem in cylinder-like domains and its applications

Abstract

We consider in this paper the pure Neumann problem in n-dimensional cylinder-like domains. We are interested in the asymptotic behaviour of the solution of this kind of problems when the domain becomes infinite in p-directions, $1 ⩽ p < n$ . We show that this solution converges exponentially to the solution of a Neumann problem in the corresponding unbounded domain. We distinguish between the case $p = 1$ and $1 < p < n$ the latter requiring a more involved analysis. For $p = 1$ we consider also the special situation when the domain and the initial data are periodic.

Keywords

Asymptotic behaviour Neumann problem stationary equation

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