On the asymptotic behaviour of the solution of parabolic problems in cylindrical domains of large size in some directions. (English) Zbl 1011.35023

The paper deals with the study of asymptotic behaviour of solutions to linear and nonlinear parabolic problems in cylindrical domains which become unbounded in one or several directions. It is shown that if the data of the problem depend only on the cross-section of the domains then the solution converges toward the solution of problems set on this cross-section. From an applicative point of view, this result enables to reduce the computations to the two-dimensional cases.


35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
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