January  2012, 11(1): i-i. doi: 10.3934/cpaa.2012.11.1i

Preface

1. 

AGIM Laboratory, FRE 3405 UJF-CNRS, TIMB Team, University J. Fourier of Grenoble (UJF), Faculty of Medicine, 38700 La Tronche

2. 

Laboratoire de Mathématiques, CNRS et Université de Paris-Sud XI, F-91405 Orsay Cedex

3. 

Graduate school of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Tokyo 153-8914

4. 

Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tamaku, Kawasaki 214-8571

Received  August 2011 Revised  September 2011 Published  September 2011

This volume deals with the mathematical modeling and the analysis of reaction-diffusion systems, as well as their applications in a number of different fields. It grew from a workshop organized by ReaDiLab, a Japan-France research collaboration unit of CNRS (Laboratoire International Associé du CNRS). This workshop took place at the University of Paris-Sud in June, 2009, bringing together many members of ReaDiLab with researchers from other French and Japanese laboratories. ReaDiLab is composed of 33 Japanese and 36 French researchers in the fields of mathematics, biology, medicine, and chemistry. Its goal is to develop mathematical modeling, analysis and numerical methods for reaction-diffusion systems arising in all those fields.

In order to understand the problems occurring in these areas of application, one should not only apply known methods, but also develop novel mathematical tools. Because of this, many results corresponding to new approaches are given in the main topics of this CPAA Special Volume, including demography and travelling waves in epidemics modelling, structured populations growth, propagation in inhomogeneous media, ecology and dry land vegetation, formation of stationary spatio-temporal patterns in reaction-diffusion systems both from a mathematical and an experimental view point, spatio-temporal dynamics of cooperation, cell migration and bacterial suspensions. This issue also includes more mathematically oriented topics such as interface dynamics, stability of non-constant stationary solutions, heterogeneity-induced spot dynamics, boundary spikes, appearance of anomalous singularities in parabolic equations, finite time blow-up, a multi-parameter inverse problem, and the numerical approximation of parabolic equations and chemotactic systems. We hope these advanced results will be useful to the community of researchers working in the domain of partial differential equations, and that they will serve as examples of mathematical modelling to those working in the different areas of application mentioned above.
Citation: Jacques Demongeot, Danielle Hilhorst, Hiroshi Matano, Masayasu Mimura. Preface. Communications on Pure and Applied Analysis, 2012, 11 (1) : i-i. doi: 10.3934/cpaa.2012.11.1i
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