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.

Full Product Details

Author:   Ralph E Showalter ,  R E Showalter
Publisher:   Dover Publications Inc.
Imprint:   Dover Publications Inc.
Dimensions:   Width: 15.20cm , Height: 0.90cm , Length: 22.70cm
Weight:   0.275kg
ISBN:  

9780486474434

ISBN 10:   0486474437
Pages:   224
Publication Date:   28 May 2010
Audience:   General/trade ,  General
Format:   Paperback
Publisher's Status:   No Longer Our Product
Availability:   In Print  
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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

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