Existence and uniqueness for a reaction-diffusion problem in infiltration |
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Authors: | Roberto Gianni Riccardo Ricci |
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Institution: | (1) Present address: Dipartimento di Matematica «Ulisse Dini», Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy;(2) Present address: Dipartimento di Matematica «F. Enriques», Università di Milano, Via C. Saldini 50, 20133 Milano, Italy |
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Abstract: | We consider a system of coupled PDE'smodeling the infiltration of a reacting fluid in a soluble porous medium. The system is made of a parabolic equation for the concentration of the dissolved material, an ODE (hyperbolic equation with characteristic x=Const.)for the porosity, and an elliptic equation for the fluid pressure. We prove the existence and uniqueness of a classical solution. The classical solution is global in time in the one-dimensional case. Global existence of a weak solution is proved for the n- dimensional case.The authors would like to acknowledge the M.U.R.S.T. Project 40% «Problemi non lineari...» and the Italia C.N.R. Strategic Project «Metodi matematici per le applicazioni industriali» for partial financial support of this work. |
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