Diffusion has been used extensively in many scientific disciplines
to model a wide variety of phenomena. The Mathematics of Diffusion
focuses on the qualitative properties of solutions to nonlinear
elliptic and parabolic equations and systems in connection with
domain geometry, various boundary conditions, the mechanism of
different diffusion rates, and the interaction between diffusion
and spatial heterogeneity. The book systematically explores the
interplay between different diffusion rates from the viewpoint of
pattern formation, particularly Turing's diffusion-driven
instability in both homogeneous and heterogeneous environments, and
the roles of random diffusion, directed movements and spatial
heterogeneity in the classical Lotka-Volterra competition systems.
Interspersed throughout the book are many simple, fundamental and
important open problems for readers to investigate.
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