On the asymptotic behaviour of the solution of parabolic problems in cylindrical domains of large size in some directions
Michel Marie Chipot, Arnaud Rougirel · Discrete and Continuous Dynamical Systems - B · 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.