August  2001, 1(3): 319-338. doi: 10.3934/dcdsb.2001.1.319

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

1. 

Institut für Mathematik, University of Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland

2. 

Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland

Received  October 2000 Revised  February 2001 Published  May 2001

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.
Citation: M. Chipot, A. Rougirel. On the asymptotic behaviour of the solution of parabolic problems in cylindrical domains of large size in some directions. Discrete and Continuous Dynamical Systems - B, 2001, 1 (3) : 319-338. doi: 10.3934/dcdsb.2001.1.319
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