Hilbert Space Methods in Partial Differential Equations
This text surveys the principal methods of solving partial differential equations. Suitable for graduate students of mathematics, engineering, and physical sciences, it requires knowledge of advanced calculus.
The initial chapter contains an elementary presentation of Hilbert space theory that provides sufficient background for understanding the rest of the book. Succeeding chapters introduce distributions and Sobolev spaces and examine boundary value problems, first- and second-order evolution equations, implicit evolution equations, and topics related to optimization and approximation. The text, which features 40 examples and 200 exercises, concludes with suggested readings and a bibliography.
1016332152
Hilbert Space Methods in Partial Differential Equations
This text surveys the principal methods of solving partial differential equations. Suitable for graduate students of mathematics, engineering, and physical sciences, it requires knowledge of advanced calculus.
The initial chapter contains an elementary presentation of Hilbert space theory that provides sufficient background for understanding the rest of the book. Succeeding chapters introduce distributions and Sobolev spaces and examine boundary value problems, first- and second-order evolution equations, implicit evolution equations, and topics related to optimization and approximation. The text, which features 40 examples and 200 exercises, concludes with suggested readings and a bibliography.
12.95 In Stock
Hilbert Space Methods in Partial Differential Equations

Hilbert Space Methods in Partial Differential Equations

by Ralph E. Showalter
Hilbert Space Methods in Partial Differential Equations

Hilbert Space Methods in Partial Differential Equations

by Ralph E. Showalter

eBook

$12.95 

Available on Compatible NOOK devices, the free NOOK App and in My Digital Library.
WANT A NOOK?  Explore Now

Related collections and offers

LEND ME® See Details

Overview

This text surveys the principal methods of solving partial differential equations. Suitable for graduate students of mathematics, engineering, and physical sciences, it requires knowledge of advanced calculus.
The initial chapter contains an elementary presentation of Hilbert space theory that provides sufficient background for understanding the rest of the book. Succeeding chapters introduce distributions and Sobolev spaces and examine boundary value problems, first- and second-order evolution equations, implicit evolution equations, and topics related to optimization and approximation. The text, which features 40 examples and 200 exercises, concludes with suggested readings and a bibliography.

Product Details

ISBN-13: 9780486135793
Publisher: Dover Publications
Publication date: 09/12/2011
Sold by: Barnes & Noble
Format: eBook
Pages: 224
File size: 40 MB
Note: This product may take a few minutes to download.

Table of Contents


I. Elements of Hilbert Space
Linear Algebra
Convergence and Continuity
Completeness
Hilbert Space
Dual Operators; Identifications
Uniform Boundedness; Weak Compactness
Expansion in Eigenfunctions
II. Distributions and Sobolev Spaces
Distributions
Sobolev Spaces
Trace
Sobolev's Lemma and Imbedding
Density and Compactness
III. Boundary Value Problems
Introduction
Forms, Operators and Green's Formula
Abstract Boundary Value Problems
Examples
Coercivity; Elliptic Forms
Regularity
Closed operators, adjoints and eigenfunction expansions
IV. First Order Evolution Equations
Introduction
The Cauchy Problem
Generation of Semigroups
Accretive Operators; two examples
Generation of Groups; a wave equation
Analytic Semigroups
Parabolic Equations
V. Implicit Evolution Equations
Introduction
Regular Equations
Pseudoparabolic Equations
Degenerate Equations
Examples
VI. Second Order Evolution Equations
Introduction
Regular Equations
Sobolev Equations
Degenerate Equations
Examples
VII. Optimization and Approximation Topics
Dirichlet's Principle
Minimization of Convex Functions
Variational Inequalities
Optimal Control of Boundary Value Problems
Approximation of Elliptic Problems
Approximation of Evolution Equations


From the B&N Reads Blog

Customer Reviews