Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium
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Laboratoire de Mathématiques, CNRS et Université de Paris-Sud, 91405 Orsay
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2.
Faculty of Mathematics, Kyushu University, 744 Motooka, Nishiku, Fukuoka, 819-0395
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Received:
01 March 2014
Revised:
01 October 2014
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35K05, 35K51, 35K57, 80A22, 80A30.
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In this paper we consider a three-component reaction-diffusion system with a fast precipitation and dissolution reaction term. We investigate its singular limit as the reaction rate tends to infinity. The limit problem is described by a combination of a Stefan problem and a linear heat equation. The rate of convergence with respect to the reaction rate is established in a specific case.
Citation: Danielle Hilhorst, Hideki Murakawa. Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium[J]. Networks and Heterogeneous Media, 2014, 9(4): 669-682. doi: 10.3934/nhm.2014.9.669
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Abstract
In this paper we consider a three-component reaction-diffusion system with a fast precipitation and dissolution reaction term. We investigate its singular limit as the reaction rate tends to infinity. The limit problem is described by a combination of a Stefan problem and a linear heat equation. The rate of convergence with respect to the reaction rate is established in a specific case.
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