Spatial Patterns: Higher Order Models in Physics and Mechanics by L.A. Peletier

Description: Spatial Patterns by L.A. Peletier, W.C. Troy 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description This monograph is divided into two parts. The first part presents unifying properties of a family of the new higher order model equations, as well as a new mathematical way of studying them. Topics include the stationary solutions of the Swift-Hohenberg equation and the extended Fisher-Kolmogorov equation which are well established fourth non-linear model equations of parabolic type. In the second part, the exposition centres around applications of the theory presented earlier. Exercises for self-study or classroom use are included. Notes A study of nonlinear higher order model equations central to the description and analysis of spatio-temporal pattern formation in the natural sciences. Unique combination of results obtained by rigorous mathematical analysis and computational studies. Text exhibits the principal families of solutions--kinks, pulses and periodic solutions, and their dependence on critical eigenvalue parameters. Exposition first focuses on a single equation to achieve optimal transparency, then branches out to wider classes of equations. Includes many exercises, open problems, recent original results, and applications to mathematical physics and mechanics. Intended for mathematicians, mathematical physicists, and graduate students. Table of Contents 1 Introduction.- 1.1 Model equations.- 1.2 The Fisher–Kolmogorov equation.- 1.3 An overview.- 1.4 Methods.- 1.5 About the presentation.- 1.6 Bibliographical notes.- I The Symmetric Bistable Equation.- 2 Real Eigenvalues.- 3 Estimates.- 4 Periodic Solutions.- 5 Kinks and Pulses.- 6 Chaotic Solutions.- 7 Variational Problems.- II Related Equations.- 8 The Asymmetric Double-Well Potential.- 9 The Swift–Hohenberg Equation.- 10 Waves in Nonlinearly Supported Beams.- References. Review "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." --Mathematical Reviews Promotional Springer Book Archives Long Description 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 Review Text "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." a?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." a?Mathematical Reviews Review Quote "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."-Mathematical Reviews Description for Sales People A study of nonlinear higher order model equations central to the description and analysis of spatio-temporal pattern formation in the natural sciences. Unique combination of results obtained by rigorous mathematical analysis and computational studies. Text exhibits the principal families of solutions--kinks, pulses and periodic solutions, and their dependence on critical eigenvalue parameters. Exposition first focuses on a single equation to achieve optimal transparency, then branches out to wider classes of equations. Includes many exercises, open problems, recent original results, and applications to mathematical physics and mechanics. Intended for mathematicians, mathematical physicists, and graduate students. Details ISBN0817641106 Author W.C. Troy Language English ISBN-10 0817641106 ISBN-13 9780817641108 Media Book Format Hardcover Series Number 45 Year 2001 Edition 1st Subtitle Higher Order Models in Physics and Mechanics Imprint Birkhauser Boston Inc Place of Publication Secaucus Country of Publication United States Edition Description 2001 Short Title HABITATS SPATIAL PATTERNS 2001 Pages 343 DOI 10.1007/b70334;10.1007/978-1-4612-0135-9 AU Release Date 2001-06-21 NZ Release Date 2001-06-21 US Release Date 2001-06-21 UK Release Date 2001-06-21 Publisher Birkhauser Boston Inc Series Progress in Nonlinear Differential Equations and Their Applications Publication Date 2001-06-21 Alternative 9781461266280 DEWEY 530.15355 Illustrations XV, 343 p. Audience Postgraduate, Research & Scholarly We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96221577;

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