@Article{JPDE-3-63, author = {N.Kenmochi , D.Kröner and M.Kubo }, title = {Periodic Solutions to Porous Media Equations of Parabolic-elliptic Type}, journal = {Journal of Partial Differential Equations}, year = {1990}, volume = {3}, number = {3}, pages = {63--77}, abstract = { This paper is concerned with a equation, which is a model of filtration in partially saturated porous media, with mixed boundary condition of Dirichlet-Neumann type {∂_tb(u) - ∇ • a [∇u + k(b(u))] = f \qquad in \quad (0, ∞) × Ω u = h(t, x) \qquad on \quad (0, ∞) × Γ_0 v • a [∇u + k(b(u))] = g(t, x) \qquad on \quad (0, ∞) × Γ_1 We have proved that there exists one and only one periodic solution of the problem under the data f, g and h with same period. Moreover, we have proved that the unique periodic solution ω is asymptotically statble in the sense that for any solution u of the problem b(u(t)) - b(ω(t)) → 0\qquad in L²(Ω) as t → ∞.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5807.html} }