UID:
almahu_9947362874202882
Umfang:
XV, 343 p.
,
online resource.
ISBN:
9781461201359
Serie:
Progress in Nonlinear Differential Equations and Their Applications ; 45
Inhalt:
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.
Anmerkung:
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.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9780817641108
Sprache:
Englisch
DOI:
10.1007/978-1-4612-0135-9
URL:
http://dx.doi.org/10.1007/978-1-4612-0135-9
URL:
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