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Hilbert Space Methods in Partial Differential Equations (Dover Books on Mathematics)

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Hilbert Space Methods in Partial Differential Equations (Dover Books on Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.

Synopsis:

This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.

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
 
 
 

Product Details

ISBN:
9780486474434
Author:
Showalter, Ralph
Publisher:
Dover Publications
Author:
Showalter, Ralph E.
Author:
Mathematics
Author:
Showalter, R. E.
Subject:
Differential Equations
Subject:
Differential equations, partial
Subject:
Hilbert space
Subject:
Transformations
Subject:
Differential Equations - Partial Differential Equations
Subject:
Hilbert Space Theory
Subject:
Boundary value problems
Subject:
Evolution equations
Subject:
General-General
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20100331
Binding:
TRADE PAPER
Language:
English
Pages:
224
Dimensions:
9 x 6 in 0.64 lb

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Product details 224 pages Dover Publications - English 9780486474434 Reviews:
"Synopsis" by ,
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
"Synopsis" by ,
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
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