On the asymptotic behaviour of the solution of parabolic problems in cylindrical domains of large size in some directions

M. Chipot; A. Rougirel

doi:10.3934/dcdsb.2001.1.319

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2001, Volume 1, Issue 3: 319-338. Doi: 10.3934/dcdsb.2001.1.319

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On the asymptotic behaviour of the solution of parabolic problems in cylindrical domains of large size in some directions

M. Chipot^1, and
A. Rougirel^2,

1.
Institut für Mathematik, University of Zürich, Winterthurerstr. 190, CH-8057 Zürich
2.
Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich

Received: October 2000

Revised: February 2001

Published: August 2001

Abstract / Introduction Related Papers Cited by

Abstract

We study the asymptotic behaviour of the solution of linear and nonlinear parabolic problems in cylindrical domains becoming unbounded in one or several directions. In particular we show that if the data depend only of the cross section of the domains the solution converges toward the solution of problems set on this cross section. In the applications this allows for instance to reduce the computations to two dimensional cases.

Keywords:

Parabolic problems,
asymptotic behaviour.

Mathematics Subject Classification: 35J25, 35J60.

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