Author(s): F. Verhulst
The composition and writing of these Lecture Notes arose from the realization of two facts. The first one is, that the approach of the fiftieth birthday of W. Eckhaus makes this an appropriate occasion to provide a collection of papers written by a number of mathematicians who were at some stage 'his students'. The papers in this book are dedicated to W. Eckhaus who has been a versatile and influential applied mathematician, working in the United States of America, in France and in the Netherlands. He has contributed fundamentally in the field of non-linear stability theory of partial differential equations, asymptotic analysis and several other branches of applied analysis. The field of asymptotic analysis especially attracted many young mathematicians in the Netherlands with as a result a rapid and varied development of the theory. This leads us to the second fact. Asymptotic analysis arose from now classical theories in celestial mechanics and fluid mechanics. The flourishing of asymptotics during the last ten years, however, took place within the discipline of applied mathematics and there is an understandable lag in the application of these new theories. One expects the subtleties of matching conditions or the estimation theory by Hilbert-space methods to take some time before being applied in the physical sciences. The realization of this second fact has provided the main idea behind the writing of most of the papers in this book: to show that asymptotic analysis as a branch of mathematics can be applied to develop new theories in'such varied fields as biology, plasmaphysics, celestial mechanics, Hamiltonian mechanics, the theory of ocean currents etc. It is in this dynamic sense that the contents of the book should reflect the title.
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