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

Article type: Research Article

Authors: Chipot, Michel^{; *} | Zube, Stephanie

Affiliations: Institute of Mathematics, University of Zurich, Winterthurerstr. 190, CH-8057 Zurich, Switzerland. E-mails: [email protected], [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

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

DOI: 10.3233/ASY-181462

Journal: Asymptotic Analysis, vol. 108, no. 3, pp. 163-185, 2018