Title Abstract parabolic evolution equations and their applications / Atsushi Yagi

Published Heidelberg ; New York : Springer, ©2010

Click on the following:
Springer eBooks
Springer Mathematics and Statistics eBooks

Copies

Description 1 online resource (xviii, 581 pages) : illustrations Series Springer monographs in mathematics, 1439-7382 Springer monographs in mathematics. Contents Contents -- Preface -- Preliminaries -- Banach Spaces -- Distance of Subsets -- Fractal Dimension -- Function Spaces with Values in a Banach Space -- Uniformly Bounded Function Spaces -- Continuously Differentiable Function Spaces -- HÃœlder Continuous Function Spaces -- Weighted HÃœlder Continuous Function Spaces -- Space of Analytic Functions -- Linear Operators -- Bounded Linear Operators -- Part of Linear Operator -- Multivalued Linear Operators -- Resolvent Equation and Pseudo-Resolvent -- Spectra of Operators -- Nonlinear Operators Contraction MappingsFréchet Differentiation -- Interpolation of Banach Spaces -- Interpolation Spaces -- Interpolation Theorem -- Adjoint Spaces and Operators -- Dual Spaces -- Adjoint Spaces -- Adjoint Operators -- Extrapolation of Hilbert Spaces -- Triplets of Spaces -- Extrapolation Theorem -- Linear Operators Associated with Sesquilinear Forms -- Sesquilinear Forms and Associated Operators -- Adjoint Forms and Adjoint Operators -- Integral Equations and Inequalities of Volterra Type -- Generalized Inequality of Gronwall Type Integral Inequality of Volterra TypeIntegral Equations of Volterra Type -- Dominate Convergence Theorem for Integral Equations -- Differential Inequalities -- Sobolev-Lebesgue Spaces -- Boundaries of Domains -- Sobolev Spaces of Integral Order -- Sobolev-Lebesgue Spaces in Rn -- Sobolev-Lebesgue Spaces in R+n or Bounded Domains -- Interpolation Property -- Embedding Theorems -- Traces -- Spaces 6Hps(Omega) and Hp-s(Omega) -- Product Spaces -- Miscellaneous Results -- Notes and Further Researches -- Sectorial Operators Sectorial Operators in Hilbert SpacesSectorial Operators Associated with Sesquilinear Form -- Sectorial Operators in L2 Spaces -- Shift Property in L2 -- Sectorial Operators in Product Spaces of L2 -- Sectorial Operators in Banach Spaces -- Sectorial Operators in Lp (1 <p <) Spaces -- Extreme Cases p = 1 and p = (infinity) -- Adjoint Operators -- Shift Property in Lp Spaces -- Sectorial Operators in Product Spaces -- Yosida Approximation -- Uniform Estimates -- Convergence -- Exponential Functions -- Analytic Semigroups -- Contraction Semigroups Adjoint SemigroupsApproximate Semigroups -- Generation of Analytic Semigroups -- Generation Results in Hilbert Spaces -- Generation Results in Lp Spaces -- Fractional Powers of Linear Operators -- Integral Formula -- Law of Exponent -- Law of Exponent, II -- Moment Inequality -- Comparison of Domains of Fractional Powers -- Fractional Powers of Adjoint Operators -- Fractional Powers and Analytic Semigroups -- Generation Theorem of Continuous Semigroups -- Purely Imaginary Powers and Square Root Problem -- Bounded Purely Imaginary Powers Summary 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 Bibliography Includes bibliographical references and index Notes Print version record Subject Evolution equations. Differential equations, Parabolic. MATHEMATICS -- Calculus. MATHEMATICS -- Mathematical Analysis. Evolution equations. Differential equations, Parabolic. Ecuaciones de evolución Differential equations, Parabolic Evolution equations Evolutionsgleichung Nichtlineare Diffusionsgleichung Parabolische Differentialgleichung Form Electronic book ISBN 9783642046315 3642046312

  Permalink