Interdisciplinary Applied Mathematics Volume 18 Editors S.S. Antman J.E. Marsden L. Sirovich S. Wiggins Geophysics and Planetary Sciences Mathematical Biology L. Glass, J.D. Murray Mechanics and Materials R.V. Kohn Systems and Control S.S. Sastry, P.S. Krishnaprasad
Problems in engineering, computational science, and the physical and biological sciences are using increasingly sophisticated mathematical techniques. Thus, the bridge between the mathematical sciences and other disciplines is heavily traveled. The correspondingly increased dialog between the disciplines has led to the establishment of the series: Interdisciplinary Applied Mathematics. The purpose of this series is to meet the current and future needs for the interaction between various science and technology areas on the one hand and mathematics on the other. This is done, firstly, by encouraging the ways that mathematics may be applied in traditional areas, as well as point towards new and innovative areas of applications; and secondly, by encouraging other scientific disciplines to engage in a dialog with mathematicians outlining their problems to both access new methods and suggest innovative developments within mathematics itself. The series will consist of monographs and high-level texts from researchers working on the interplay between mathematics and other fields of science and technology.
Interdisciplinary Applied Mathematics Volumes published are listed at the end of the book.
Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo
J.D. Murray
Mathematical Biology II: Spatial Models and Biomedical Applications Third Edition
With 298 Illustrations
Springer
J.D. Murray, FRS Emeritus Professor University of Oxford and University of Washington Box 352420 Department of Applied Mathematics Seattle, WA 98195-2420 USA Editors S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA
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J.E. Marsden Control and Dynamical Systems Mail Code 107-81 California Institute of Technology Pasadena, CA 91125 USA
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L. Sirovich Division of Applied Mathematics Brown University Providence, RI 02912 USA
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S. Wiggins School of Mathematics University of Bristol Bristol BS8 1TW UK
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c Alain Pons. Cover illustration: Mathematics Subject Classification (2000): 92B05, 92-01, 92C05, 92D30, 34Cxx Library of Congress Cataloging-in-Publication Data Murray, J.D. (James Dickson) Mathematical biology. II: Spatial models and biomedical applications / J.D. Murray.—3rd ed. p. cm.—(Interdisciplinary applied mathematics) Rev. ed. of: Mathematical biology. 2nd ed. c1993. Includes bibliographical references (p. ). ISBN 0-387-95228-4 (alk. paper) 1. Biol