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Stabilization estimates for penetrative motions in porous media
Author(s) -
Franchi Franca
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670170103
Subject(s) - porous medium , mathematics , boundary value problem , convection , norm (philosophy) , class (philosophy) , mathematical analysis , porosity , mechanics , physics , law , geology , computer science , artificial intelligence , political science , geotechnical engineering
The physical model for penetrative convection in porous media is here considered to study the effects of variation of the source parameters on the flow. In this note we study the continuous dependence upon the heat supply and the body force of the classical solutions to the initial‐boundary value problem of a heat conducting fluid through a porous solid, both for the (well‐posed) forward problem and for the (improperly posed) backward in time one. For the former problem we obtain a result of continuous dependence with respect to the L 2 norm; while for the latter we prove a result of Hölder continuity in a suitably constrained class of solutions.