Publisher:

Chapman & Hall/CRC

Number of Pages:

268

Price:

79.95

ISBN:

9781439880838

Date Received:

Friday, August 3, 2012

Reviewable:

No

Reviewer Email Address:

Publication Date:

2012

Format:

Hardcover

Audience:

Category:

Textbook

**Introduction to Functional Analysis in Applications **Example 1: Heat Equation

Some Preliminaries: Hilbert, Banach, and Other Spaces Useful in Operator Theory

Return to Example 1: Heat Equation

Example 2: General Transport Equation

Example 3: Delay Systems–Insect/Insecticide Models

Example 4: Probability Measure Dependent Systems — Maxwell’s Equations

Example 5: Structured Population Models

** **

**Semigroups and Infinitesimal Generators **Basic Principles of Semigroups

Infinitesimal Generators

** **

**Generators **Introduction to Generation Theorems

Hille-Yosida Theorems

Results from the Hille-Yosida Proof

Corollaries to Hille-Yosida

Lumer-Phillips and Dissipative Operators

Examples Using Lumer-Phillips Theorem

** **

**Adjoint Operators and Dual Spaces **Adjoint Operators

Dual Spaces and Strong, Weak, and Weak* Topologies

Examples of Spaces and Their Duals

Return to Dissipativeness for General Banach Spaces

More on Adjoint Operators

Examples of Computing Adjoints

** **

**Gelfand Triple, Sesquilinear Forms, and Lax-Milgram**

Example 6: The Cantilever Beam

The Beam Equation in the Form *x* derivative = *Ax* + *F*

Gelfand Triples

Sesquilinear Forms

Lax-Milgram (Bounded Form)

Lax-Milgram (Unbounded Form)

Summary Remarks and Motivation

** **

**Analytic Semigroups**Example 1: The Heat Equation (again)

Example 2: The Transport Equation (again)

Example 6: The Beam Equation (again)

Summary of Results on Analytic Semigroup Generation by Sesquilinear Forms

Tanabe Estimates (on "Regular Dissipative Operators")

Infinitesimal Generators in a General Banach Space

**
**

**Abstract Cauchy Problems**

**General Second-Order Systems**Introduction to Second-Order Systems

Results for

Results for

Stronger Assumptions for

** **

**Weak Formulations for Second-Order Systems**Model Formulation

Discussion of the Model

Theorems 9.1 and 9.2: Proofs

** **

**Inverse or Parameter Estimation Problems**Approximation and Convergence

Some Further Remarks

**
**

**"Weak" or "Variational Form"**

**Finite Element Approximations and the Trotter-Kato Theorems**

Finite Elements

Trotter-Kato Approximation Theorem

** **

**Delay Systems: Linear and Nonlinear **Linear Delay Systems and Approximation

Modeling of Viral Delays in HIV Infection Dynamics

Nonlinear Delay Systems

State Approximation and Convergence for Nonlinear Delay Systems

Fixed Delays versus Distributed Delays

** **

**Weak* Convergence and the Prohorov Metric in Inverse Problems**

Populations with Aggregate Data, Uncertainty, and PBM

A Prohorov Metric Framework for Inverse Problems

Metrics on Probability Spaces

Example 5: The Growth Rate Distribution Model and Inverse Problem in Marine Populations

** **

**The Prohorov Metric in Optimization and Optimal Design Problems**

Two Player Min-Max Games with Uncertainty

Optimal Design Techniques

Generalized Curves and Relaxed Controls of Variational Theory

Preisach Hysteresis in Smart Materials

NPML and Mixing Distributions in Statistical Estimation

** **

**Control Theory for Distributed Parameter Systems **Motivation

Abstract Formulation

Infinite Dimensional LQR Control: Full State Feedback

The Finite Horizon Control Problem

The Infinite Horizon Control Problem

** **

**Families of Approximate Control Problems**The Finite Horizon Problem Approximate Control Gains

The Infinite Horizon Problem Approximate Control Gains

**
**

**References**

Index

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