Sinossi
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.
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Recensione
"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
Contenuti
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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Spatial Patterns: Higher Order Models in Physics and Mechanics (Progress in Nonlinear Differential Equations and Their Applications)
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Spatial Patterns: Higher Order Models in Physics and Mechanics (Progress in Nonlinear Differential Equations and Their Applications)
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Spatial Patterns : Higher Order Models in Physics and Mechanics
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Spatial Patterns
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Birkhäuser Boston Okt 2012, 2012
ISBN 10: 1461266289
ISBN 13: 9781461266280
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 364 pp. Englisch. Codice articolo 9781461266280
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Spatial Patterns: Higher Order Models in Physics and Mechanics
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ISBN 10: 1461266289
ISBN 13: 9781461266280
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 clo. Codice articolo 4189273
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Spatial Patterns
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Birkhäuser Boston, Birkhäuser Boston Okt 2012, 2012
ISBN 10: 1461266289
ISBN 13: 9781461266280
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Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germania
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Taschenbuch. Condizione: Neu. Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 364 pp. Englisch. Codice articolo 9781461266280
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Spatial Patterns | Higher Order Models in Physics and Mechanics
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Taschenbuch. Condizione: Neu. Spatial Patterns | Higher Order Models in Physics and Mechanics | W. C. Troy (u. a.) | Taschenbuch | xv | Englisch | 2012 | Birkhäuser Boston | EAN 9781461266280 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Codice articolo 106029387
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Spatial Patterns : Higher Order Models in Physics and Mechanics
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Birkhäuser Boston, Birkhäuser Boston, 2012
ISBN 10: 1461266289
ISBN 13: 9781461266280
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9781461266280
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