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Discovering Evolution Equations with Applications Volume 1: Deterministic Equations

Publisher: 
Chapman & Hall/CRC
Number of Pages: 
448
Price: 
99.95
ISBN: 
9781420092073
Date Received: 
Monday, August 16, 2010
Reviewable: 
No
Include In BLL Rating: 
No
Reviewer Email Address: 
Mark A. McKibben
Series: 
Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series
Publication Date: 
2011
Format: 
Hardcover
Category: 
Monograph

A Basic Analysis Toolbox
Some Basic Mathematical Shorthand
Set Algebra
Functions
The Space (R, |·|)
Sequences in (R, |·|)
The Spaces (RN, ||·||RN) and (MN(R), ||·||MN(R))
Abstract Spaces
Elementary Calculus in Abstract Spaces
Some Elementary ODEs
Looking Ahead
Guidance for Exercises

Homogenous Linear Evolution Equations in RN
Motivation by Models
The Matrix Exponential
The Homogenous Cauchy Problem: Well-Posedness
Perturbation and Convergence Results
A Glimpse at Long-Term Behavior
Looking Ahead
Guidance for Exercises

Abstract Homogenous Linear Evolution Equations
Linear Operators
Motivation by Models
Introducing Semigroups
The Abstract Homogenous Cauchy Problem
Generation Theorems
A Useful Perturbation Result
Some Approximation Theory
A Brief Glimpse at Long-Term Behavior
An Important Look Back
Looking Ahead
Guidance for Exercises

Nonhomogenous Linear Evolution Equations
Finite-Dimensional Setting
Infinite-Dimensional Setting
Introducing Two New Models
Looking Ahead
Guidance for Exercises

Semi-Linear Evolution Equations
Motivation by Models
More Tools from Functional Analysis
Some Essential Preliminary Considerations
Growth Conditions
Theory for Lipschitz-Type Forcing Terms
Theory for Non-Lipschitz-Type Forcing Terms
Theory under Compactness Assumptions
A Summarizing Look Back
Looking Ahead
Guidance for Exercises

Functional Evolution Equations
Motivation by Models
Functionals
Theory in the Lipschitz Case
Theory under Compactness Assumptions
Models—New and Old
Looking Ahead
Guidance for Exercises

Implicit Evolution Equations
Sobolev-Type Equations
Neutral Evolution Equations
Looking Ahead
Guidance for Exercises

Delay Evolution Equations
Motivation by Models
Setting and Formulation of the Problem
Theory for Lipschitz-Type Forcing Terms
Theory for Non-Lipschitz-Type Forcing Terms
Implicit Delay Evolution Equations
Other Forms of Delay
Models—New and Old
An Important Look Back!
Looking Ahead
Guidance for Exercises

Nonlinear Evolution Equations
A Wealth of New Models
Comparison of the Linear and Nonlinear Settings
The Crandall–Liggett Theory
A Quick Look at Nonlinear Evolution Inclusions
Some Final Comments
Guidance for Exercises

Nonlocal Evolution Equations
Introductory Remarks
Motivation by Models
Some Abstract Theory
Final Comments

Beyond Volume 1…
Three New Classes of Evolution Equations
Next Stop… Stochastic Evolution Equations!: The Preface to Volume 2

Bibliography

Index

Publish Book: 
Modify Date: 
Thursday, November 18, 2010

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