Abstract
We study a phenomenon of growth and dissolution occurring in processes of mineralization (metasomatism) in geology. The heterogeneous system considered is a grain exchanging mass with a liquid solution impregnating a porous medium which gives rise to a source term. The system is bounded, of spherical symmetry, and the concentration is fixed on the external boundary. The evolution of the concentration of the liquid solution is described by a moving boundary problem. The associated stationary problem is a free boundary problem which may exhibit zero, one, two, or three solutions. A study of the stability by means of the associated evolution problem is set up, mainly by numerical techniques. In the cases studied, uniqueness in the stationary problem implies instability. When three solutions occur, we observe two unstable solutions, and only one stable solution.
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