عنوان

Theory and applications of abstract semilinear cauchy problems /

(Number (ISBN

3030015068

(Number (ISBN

9783030015060

Erroneous ISBN

303001505X

Erroneous ISBN

9783030015053

Title Proper

Theory and applications of abstract semilinear cauchy problems /

General Material Designation

[Book]

First Statement of Responsibility

Pierre Magal, Shigui Ruan.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

[2018]

Date of Publication, Distribution, etc.

©2018

Specific Material Designation and Extent of Item

1 online resource

Series Title

Applied mathematical sciences ;

Volume Designation

volume 201

Text of Note

Includes bibliographical references and index.

Text of Note

Intro; Foreword; Preface; Contents; Acronyms; 1 Introduction; 1.1 Ordinary Differential Equations; 1.1.1 Spectral Properties of Matrices; 1.1.2 State Space Decomposition; 1.1.3 Semilinear Systems; 1.2 Retarded Functional Differential Equations; 1.2.1 Existence and Uniqueness of Solutions; 1.2.2 Linearized Equation at an Equilibrium; 1.2.3 Characteristic Equations; 1.2.4 Center Manifolds; 1.3 Age-Structured Models; 1.3.1 Volterra Formulation; 1.3.2 Age-Structured Models Without Birth; 1.3.3 Age-Structured Models with Birth; 1.3.4 Equilibria and Linearized Equations

Text of Note

1.3.5 Age-Structured Models Reduce to DDEs and ODEs1.4 Abstract Semilinear Formulation; 1.4.1 Functional Differential Equations; 1.4.2 Age-Structured Models; 1.4.3 Size-Structured Models; 1.4.4 Partial Functional Differential Equations; 1.5 Remarks and Notes; 2 Semigroups and Hille-Yosida Theorem; 2.1 Semigroups; 2.1.1 Bounded Case; 2.1.2 Unbounded Case; 2.2 Resolvents; 2.3 Infinitesimal Generators; 2.4 Hille-Yosida Theorem; 2.5 Nonhomogeneous Cauchy Problem; 2.6 Examples; 2.7 Remarks and Notes; 3 Integrated Semigroups and Cauchy Problems with Non-dense Domain; 3.1 Preliminaries

Text of Note

3.2 Integrated Semigroups3.3 Exponentially Bounded Integrated Semigroups; 3.4 Existence of Mild Solutions; 3.5 Bounded Perturbation; 3.6 The Hille-Yosida Case; 3.7 The Non-Hille-Yosida Case; 3.8 Applications to a Vector Valued Age-Structured Model in Lp; 3.9 Remarks and Notes; 4 Spectral Theory for Linear Operators; 4.1 Basic Properties of Analytic Maps; 4.2 Spectra and Resolvents of Linear Operators; 4.3 Spectral Theory of Bounded Linear Operators; 4.4 Essential Growth Bound of Linear Operators; 4.5 Spectral Decomposition of the State Space

Text of Note

4.6 Asynchronous Exponential Growth of Linear Operators4.7 Remarks and Notes; 5 Semilinear Cauchy Problems with Non-dense Domain; 5.1 Introduction; 5.2 Existence and Uniqueness of a Maximal Semiflow: The Blowup Condition; 5.3 Positivity; 5.4 Lipschitz Perturbation; 5.5 Differentiability with Respect to the State Variable; 5.6 Time Differentiability and Classical Solutions; 5.7 Stability of Equilibria; 5.8 Remarks and Notes; 6 Center Manifolds, Hopf Bifurcation, and Normal Forms; 6.1 Center Manifold Theory; 6.1.1 Existence of Center Manifolds; 6.1.2 Smoothness of Center Manifolds

Text of Note

6.2 Hopf Bifurcation6.2.1 State Space Decomposition; 6.2.2 Hopf Bifurcation Theorem; 6.3 Normal Form Theory; 6.3.1 Nonresonant Type Results; 6.3.2 Normal Form Computation; 6.4 Remarks and Notes; 7 Functional Differential Equations; 7.1 Retarded Functional Differential Equations; 7.1.1 Integrated Solutions and Spectral Analysis; 7.1.2 Projectors on the Eigenspaces; 7.1.3 Hopf Bifurcation; 7.2 Neutral Functional Differential Equations; 7.2.1 Spectral Theory; 7.2.2 Projectors on the Eigenspaces; 7.3 Partial Functional Differential Equations

0

8

8

8

8

Text of Note

Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.--

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783030015060

Title

Theory and applications of abstract semilinear cauchy problems.

International Standard Book Number

9783030015053

Cauchy problem.

Differential equations, Parabolic.

Differential equations.

Evolution equations.

Semigroup algebras.

Cauchy problem.

Differential calculus & equations.

Differential equations, Parabolic.

Differential equations.

Evolution equations.

MATHEMATICS-- Essays.

MATHEMATICS-- Pre-Calculus.

MATHEMATICS-- Reference.

Semigroup algebras.

MAT-- 023000

MAT-- 026000

MAT-- 039000

PBKJ

PBKJ

Number

Edition

Class number

Class number

Book number

Book number

Magal, Pierre

Ruan, Shigui,1963-

Date of Transaction

20200823073115.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y