In the spirit of the recent work of Ames, Payne, and Schaefer [SIAM J. Math. Anal., 24 (1993), pp. 97--116], the decay of flow in a porous medium through a semi-infinite pipe is investigated. The analysis presented in this paper is based on the Brinkman--Forchheimer model. In establishing decay estimate and bounds for the total weighted energy, the nonlinear term in the model equation leads to difficulties which were not encountered in the paper cited above.
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Chadam et al. (1997) studied this question.
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