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Spatial Patterns - Higher Order Models in Physics and Mechanics (Paperback, Softcover reprint of the original 1st ed. 2001)
Loot Price: R1,602
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Spatial Patterns - Higher Order Models in Physics and Mechanics (Paperback, Softcover reprint of the original 1st ed. 2001)
Series: Progress in Nonlinear Differential Equations and Their Applications, 45
Expected to ship within 10 - 15 working days
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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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