The author proves the existence of weak periodic solutions to a nonlinear parabolic problem with applications in hydrology. The proof of the main result is based on the Schauder fixed point theorem applied to the Poincaré map of the associated initial boundary value problem. For this aim, by means of the standard parabolic regularization, it is constructed the approximating problem and it is proved the existence and the uniqueness of the solution to this problem. After deducing uniform estimates it is justified the convergence of the approximated sequence of solutions. We point out that uniform estimates are obtained by constructing subsolutions and supersolutions of travelling-wave type.
For the entire collection see [Zbl 0905.00059].