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This work of applied mathematics focuses on the functional study of the nonlinear boundary value problems relating to water flow in porous media, a topic which has not up to now been explored in book form. The author shows that abstract theory may be sometimes easier and richer in consequences for applications than standard classical approaches are. The volume deals with diffusion type models, emphasizing the mathematical treatment of their nonlinear aspects.
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Functional Approach to Nonlinear Models of Water Flow in Soils MATHEMATICAL MODELLING: Theory and Applications VOLUME 21 This series is aimed at publishing work dealing with the definition, development and application of fundamental theory and methodology, computational and algorithmic implementations and comprehensive empirical studies in mathematical modelling. Work on new mathematics inspired by the construction of mathematical models, combining theory and experiment and furthering the understanding of the systems being modelled are particularly welcomed. Manuscripts to be considered for publication lie within the following, non-exhaustive list of areas: mathematical modelling in engineering, industrial mathematics, control theory, operations research, decision theory, economic modelling, mathematical programmering, mathematical system theory, geophysical sciences, climate modelling, environmental processes, mathematical modelling in psychology, political science, sociology and behavioural sciences, mathematical biology, mathematical ecology, image processing, computer vision, artificial intelligence, fuzzy systems, and approximate reasoning, genetic algorithms, neural networks, expert systems, pattern recognition, clustering, chaos and fractals. Original monographs, comprehensive surveys as well as edited collections will be considered for publication. Editor: R. Lowen (Antwerp, Belgium) Editorial Board: J.-P. Aubin (Université de Paris IX, France) E. Jouini (Université Paris IX - Dauphine, France) G.J. Klir (New York, U.S.A.) P.G. Mezey (Saskatchewan, Canada) F. Pfeiffer (München, Germany) A. Stevens (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany) H.-J. Zimmerman (Aachen, Germany) The titles published in this series are listed at the end of this volume. Functional Approach to Nonlinear Models of Water Flow in Soils by Gabriela Marinoschi Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Bucharest, Romania A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-10 ISBN-13 ISBN-10 ISBN-13 1-4020-4879-3 (HB) 978-1-4020-4879-1 (HB) 1-4020-4880-7 (e-book) 978-1-4020-4880-7 (e-book) Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com Printed on acid-free paper All Rights Reserved © 2006 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands. Contents Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Introduction-motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Part I Modelling water infiltration in soils 1 Brief overview of unsaturated flow concepts . . . . . . . . . . . . . . . 3 1.1 Some basic definitions in the unsaturated flow . . . . . . . . . . . . . . . 3 1.2 Richards’ equation . . . . . . . . . . . . . . . . . . . . .