Periodic Solutions to Porous Media Equations of Parabolic-elliptic Type

Periodic Solutions to Porous Media Equations of Parabolic-elliptic Type

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