Preface

Abstract

This volume deals with the mathematical modeling and the analysis ofreaction-diffusion systems, as well as their applications in a numberof different fields. It grew from a workshop organizedby ReaDiLab, a Japan-France research collaboration unit of CNRS(Laboratoire International Associé du CNRS). This workshop tookplace at the University of Paris-Sud in June, 2009, bringing togethermany members of ReaDiLab with researchers from other French and Japaneselaboratories. ReaDiLab is composed of 33 Japanese and 36 French researchersin the fields of mathematics, biology, medicine, andchemistry. Its goal is to develop mathematical modeling, analysis andnumerical methods for reaction-diffusion systems arising in all thosefields.In order to understand the problems occurring in these areas of application,one should not only apply known methods, but also developnovel mathematical tools. Because of this, many results corresponding tonew 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, ecologyand dry land vegetation, formation of stationary spatio-temporal patterns inreaction-diffusion systems both from a mathematical and an experimental viewpoint, spatio-temporal dynamics of cooperation, cell migration and bacterialsuspensions. This issue also includes more mathematically oriented topicssuch as interface dynamics, stability of non-constant stationary solutions,heterogeneity-induced spot dynamics, boundary spikes, appearance ofanomalous singularities in parabolic equations, finite time blow-up, amulti-parameter inverse problem, and the numerical approximation ofparabolic equations and chemotactic systems. We hope these advanced resultswill be useful to the community of researchers working in the domain ofpartial differential equations, and that they will serve as examplesof mathematical modelling to those working in the different areas ofapplication mentioned above.