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Field name	Details
Dewey Class	515.353
Title	Abstract Parabolic Evolution Equations and their Applications ([Ebook]) / by Atsushi Yagi.
Author	Yagi, Atsushi
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2010.
Physical Details	: online resource.
Series	Springer monographs in mathematics 1439-7382
ISBN	9783642046315
Summary Note	The semigroup methods are known as a powerful tool for analyzing nonlinear diffusion equations and systems. The author has studied abstract parabolic evolution equations and their applications to nonlinear diffusion equations and systems for more than 30 years. He gives first, after reviewing the theory of analytic semigroups, an overview of the theories of linear, semilinear and quasilinear abstract parabolic evolution equations as well as general strategies for constructing dynamical systems, attractors and stable-unstable manifolds associated with those nonlinear evolution equations. In the second half of the book, he shows how to apply the abstract results to various models in the real world focusing on various self-organization models: semiconductor model, activator-inhibitor model, B-Z reaction model, forest kinematic model, chemotaxis model, termite mound building model, phase transition model, and Lotka-Volterra competition model. The process and techniques are explained concretely in order to analyze nonlinear diffusion models by using the methods of abstract evolution equations. Thus the present book fills the gaps of related titles that either treat only very theoretical examples of equations or introduce many interesting models from Biology and Ecology, but do not base analytical arguments upon rigorous mathematical theories.:
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-642-04631-5
Links to Related Works	Subject References: Differentiable dynamical systems . Differential equations, Parabolic . Differential equations, Partial . Dynamical systems and ergodic theory . Mathematical Biology in General . Mathematics . Partial differential equations . Authors: Yagi, Atsushi . Corporate Authors: SpringerLink (Online service) . Series: Springer monographs in mathematics . Classification: 515.353 . 515.353 (DDC 23) .

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Abstract Parabolic Evolution Equations and their Applications

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