The study of spatial patterns in extended systems, and their evolution with time, poses challenging questions for physicists and mathematicians alike. Waves on water, pulses in optical fibers, periodic structures in alloys, folds in rock formations, and cloud patterns in the sky: patterns are omnipresent in the world around us. Their variety and complexity make them a rich area of study. In the study of these phenomena an important role is played by well-chosen model equations, which are often simpler than the full equations describing the physical or biological system, but still capture its essential features. Through a thorough analysis of these model equations one hopes to glean a better under- standing of the underlying mechanisms that are responsible for the formation and evolution of complex patterns. Classical model equations have typically been second-order partial differential equations. As an example we mention the widely studied Fisher-Kolmogorov or Allen-Cahn equation, originally proposed in 1937 as a model for the interaction of dispersal and fitness in biological populations. As another example we mention the Burgers equation, proposed in 1939 to study the interaction of diffusion and nonlinear convection in an attempt to understand the phenomenon of turbulence. Both of these are nonlinear second-order diffusion equations.
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"The book is on the one hand written for mathematicians and mathematical physicists, who want to learn about this fascinating subject, and on the other hand also accessible to graduate students. One finds a large amount of exercises and open problems that can serve as a starting point for further research . . . The authors have produced a well-written book, which gives a good picture of what is known about the canonical equation."
—Quantum Information and Computation
"The book is very well written in a very clear and readable style, which makes it accessible to a nonspecialist or graduate student. There are a large number of exercises, which fill in details of proofs or provide illuminating examples or straightforward generalisations as well as a good number of open problems. There are also a large number of numerically computed graphs of branching curves and bifurcation curves throughout the book, which provide insights into the mathematically formulated results. The book is a valuable contribution to the literature, for both the specialist and the nonspecialist reader."
Preface Outline 1. Introduction Part I: The Symmetric Bistable Equation 2. Real Eigenvalues 3. Estimates 4. Periodic Solutions 5. Kinks and Pulses 6. Chaotic Solutions 7. Variational Problems Part II: Related Equations 8. The Asymmetric Double-Well Potential 9. The Swift--Hohenberg Equation 10. Waves in Nonlinearly Supported Beams References Index
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Descrizione libro Birkhäuser, 2001. Hardcover. Condizione libro: New. 2001. Codice libro della libreria DADAX0817641106
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Descrizione libro Birkhäuser, 2001. Hardcover. Condizione libro: New. book. Codice libro della libreria 0817641106
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Descrizione libro Birkhäuser. Condizione libro: New. 0817641106 This is an International Edition. Brand New, Hardcover, Delivery within 6-14 business days, Similar Contents as U.S Edition, ISBN and Cover design may differ, printed in Black & White. Choose Expedited shipping for delivery within 3-8 business days. We do not ship to PO Box, APO , FPO Address. In some instances, subjects such as Management, Accounting, Finance may have different end chapter case studies and exercises. International Edition Textbooks may bear a label "Not for sale in the U.S. or Canada" and "Content may different from U.S. Edition" - printed only to discourage U.S. students from obtaining an affordable copy. The U.S. Supreme Court has asserted your right to purchase international editions, and ruled on this issue. Access code/CD is not provided with these editions , unless specified. We may ship the books from multiple warehouses across the globe, including India depending upon the availability of inventory storage. Customer satisfaction guaranteed. Codice libro della libreria OA9780817641108
Descrizione libro BirkhÇÏuser, 2001. Hardback. Condizione libro: NEW. 9780817641108 Hardback, This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0285662