Discovering Evolution Equations with

Most books written on evolution equations either provide a thorough in-depth treatment of a particular class of equations for beginners or present an assimilation of materials devoted to a very particular timely research direction. This volume offers an engaging, accessible account of a rudimentary core of theoretical results that should be understood by anyone studying evolution equations. The text gradually builds readers' intuition and the material culminates in a discussion of an area of active research. The author's conversational style sets the stage for the next step of theoretical development, allowing readers to see the big picture.

A Basic Analysis Toolbox
Some Basic Mathematical Shorthand
Set Algebra
Functions
The Space (R, · )
Sequences in (R, · )
The Spaces (R^N, · _R^N) and (M^N(R), · _M^N_(R))
Abstract Spaces
Elementary Calculus in Abstract Spaces
Some Elementary ODEs
Looking Ahead
Guidance for Exercises
Homogenous Linear Evolution Equations in R^N
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
Table of Contents provided by Publisher. All Rights Reserved.

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Discovering Evolution Equations with Applications

Summary

Table of Contents

Supplemental Materials