Year: 1990
Journal of Partial Differential Equations, Vol. 3 (1990), Iss. 3 : pp. 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 → ∞.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1990-JPDE-5807
Journal of Partial Differential Equations, Vol. 3 (1990), Iss. 3 : pp. 63–77
Published online: 1990-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Filtration equation