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IMA Journal of Applied Mathematics Advance Access originally published online on December 6, 2007
IMA Journal of Applied Mathematics 2008 73(2):393-411; doi:10.1093/imamat/hxm060
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A Stefan problem modelling crystal dissolution and precipitation

T. L. van Noorden{dagger} and I. S. Pop{ddagger}

Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, PO Box 513, 5600 MB Eindhoven, The Netherlands

{dagger} Corresponding author. Email: t.l.v.noorden{at}tue.nl

{ddagger} Email: i.pop{at}tue.nl

Received on October 12, 2006; Accepted on October 16, 2007

A simple 1D model for crystal dissolution and precipitation is presented. The model equations resemble a one-phase Stefan problem and involve non-linear and multivalued exchange rates at the free boundary. The original equations are formulated on a variable domain. By transforming the model to a fixed domain and applying a regularization, we prove the existence and uniqueness of a solution. The paper is concluded by numerical simulations.

Keywords: evolution system; existence; free boundary; multivalued rate; regularization; Stefan problem; uniqueness.


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