Affiliations: Department of Mathematics, University of Arizona, Tuscon, Arizona, 85721 USA | Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4Kl Canada | Departments of Chemistry and Geology, Indiana University, Bloomington, Ind., 47405 USA
Note: [] Correspondence to: J. Xin, Department of Mathematics, University of Arizona, Tuscon, Arizona, 85721 USA.
Note: [] The authors would like to thank F. Clarke and the members and staff of the CRM, Montreal for their kind hospitality during the summer of 1990 when this work was initiated. They would also like to acknowledge financial support from the CRM and FCAR, Quebec, through their funding of this focal period on Non-Linear PDE's and Applications.
Note: [] Supported by NSERC (Canada).
Note: [] Supported by NSERC (Canada).
Abstract: A model of reactive flow in a layered porous medium is considered in which the layering is represented by small-scale periodic structure. A novel form of homogenization analysis is presented, combining geometric optics and multiple scales expansions together with matched asymptotics to derive an effective free boundary problem for the motion of the reactive interface. Applications of the effective free boundary equations are given in which travelling wave solutions and the stability of shape perturbations are considered.
