Analytic semigroups and semilinear initial boundary value problems / Kazuaki Taira, Waseda University, Japan.

Format:

Book

Author/Creator:

Taira, Kazuaki, author.

Series:

London Mathematical Society lecture note series ; 434.

London Mathematical Society lecture note series ; 434

Language:

English

Subjects (All):

Differential equations, Parabolic.

Boundary value problems.

Semigroups.

Physical Description:

1 online resource (xvi, 331 pages) : digital, PDF file(s).

Edition:

Second edition.

Other Title:

Analytic Semigroups & Semilinear Initial Boundary Value Problems

Place of Publication:

Cambridge : Cambridge University Press, 2016.

Language Note:

English

Summary:

This second edition explores the relationship between elliptic and parabolic initial boundary value problems, for undergraduate and graduate students.

Contents:

Cover; Series page; Title page; Copyright page; Dedication; Contents; Preface to the Second Edition; Preface to the First Edition; 1 Introduction and Main Results; 2 Preliminaries from Functional Analysis; 3 Theory of Analytic Semigroups; 4 Sobolev Imbedding Theorems; 5 L[sup(p)] Theory of Pseudo-Differential Operators; 6 L[sup(p)] Approach to Elliptic Boundary Value Problems; 7 Proof of Theorem 1.1; 8 Proof of Theorem 1.2; 9 Proof of Theorems 1.3 and 1.4; Appendix A The Laplace Transform; Appendix B The Maximum Principle; Appendix C Vector Bundles; References; Index

2.10 The Hilbert-Schmidt theory3.1 Generation theorem for analytic semigroups; 3.2 Fractional powers; 3.3 The linear Cauchy problem; 3.4 The semilinear Cauchy problem; 4.1 Hölder spaces and Sobolev spaces; 4.2 Interpolation theorems; 4.3 Imbeddings of the spaces W[sup(m,p)](R[sup(n)]); 4.4 Imbeddings of the spaces W[sup(m,p)](Ω); 4.5 Trace theorems; 4.6 Jump formulas; 4.7 Regular distributions with respect to one variable; 5.1 Generalized Sobolev spaces and Besov spaces; 5.2 Fourier integral operators; 5.3 Pseudo-differential operators; 6.1 The Dirichlet problem

2.3.2 Continuity of linear operators2.3.3 Topologies of linear operators; 2.3.4 The Banach-Steinhaus theorem; 2.4.1 Finite dimensional spaces; 2.4.2 The Hahn-Banach extension theorem; 2.4.3 Dual spaces; 2.4.4 Annihilators; 2.4.5 Dual spaces of normed factor spaces; 2.4.6 Bidual spaces; 2.4.7 Transpose operators; 2.7.1 Compact operators; 2.7.2 Spectral analysis of compact operators; 2.9.1 Orthogonality; 2.9.2 The closest-point theorem and applications; 2.9.3 Orthonormal sets; 2.9.4 Adjoint operators; 3.3.1 The homogeneous case; 3.3.2 The non-homogeneous case

3.4.1 The space E[sub(α)] of fractional powers

Notes:

Title from publisher's bibliographic system (viewed on 05 Apr 2016).

Includes bibliographical references and index.

ISBN:

1-316-75699-8

1-316-75771-4

1-316-75783-8

1-316-75795-1

1-316-75807-9

1-316-75843-5

1-316-72975-3