February  2012, 5(1): i-i. doi: 10.3934/dcdss.2012.5.1i

Preface

1. 

Department of Mathematics, Faculty of Education, Gifu University, Yanagido 1-1, Gifu, 501-1193

2. 

CNRS and Laboratoire de Mathématiques, Université de Paris-Sud 11, F-91405 Orsay Cedex

3. 

Institute for Advanced Study of Mathematical Sciences, Meiji University, 1-1 Higashi Mita, Tama-ku, Kawasaki, 214-8571

4. 

Department of Mathematics and Computer Science, Eindhoven University of Technology, Institute of Complex Molecular Systems (ICMS), P.O. Box 513, 5600 MB Eindhoven

Published  February 2011

This issue is focussed on the modeling, analysis and simulation of fast reaction-slow transport scenarios as well as corresponding fast-reaction limits. Within this framework, internal sharp and thin reaction layers form and travel through the spatial domain often producing unexpected effects. Such situations appear in a variety of significant applications; for example flame propagation in combustion, segregation and aggregation of biological individuals, chemical attack on reactive porous materials (such as concrete or natural stone), dissolution and precipitation reactions in minerals, tumor growth, grain boundary motion, and temperature-induced phase transitions in shape-memory alloys represent typical cases in which the fast process is localized within a a priori unknown internal active layer.

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