Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium

Danielle Hilhorst; Hideki Murakawa

doi:10.3934/nhm.2014.9.669

Article Contents

2014, Volume 9, Issue 4: 669-682. Doi: 10.3934/nhm.2014.9.669

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Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium

Danielle Hilhorst^1, and
Hideki Murakawa^2,

1.
Laboratoire de Mathématiques, CNRS et Université de Paris-Sud, 91405 Orsay
2.
Faculty of Mathematics, Kyushu University, 744 Motooka, Nishiku, Fukuoka, 819-0395

Received: March 2014

Revised: October 2014

Published: December 2014

Abstract / Introduction Related Papers Cited by

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.

Keywords:

Mathematics Subject Classification: 35K05, 35K51, 35K57, 80A22, 80A30.

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References

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