Hilbert Space Methods in Partial Differential Equations

Hilbert Space Methods in Partial Differential Equations
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2010-03
ISBN: 0486474437 或 9780486474434
定价: 102.00
装帧: 平装
开本: 其他
页数: 224页
正文语种: 英语
  • 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.
                                     I. Elements of Hilbert Space   Linear Algebra   Convergence and Continuity   Completeness   Hilbert Space   Dual Operators; Identifications   Uniform Boundedness; Weak Compactness   Expansion in EigenfunctionsII. Distributions and Sobolev Spaces    Distributions    Sobolev Spaces    Trace    Sobolev's Lemma and Imbedding    Density and CompactnessIII. Boundary Value Problems      Introduction      Forms, Operators and Green's Formula      Abstract Boundary Value Problems      Examples      Coercivity; Elliptic Forms      Regularity      Closed operators, adjoints and eigenfunction expansionsIV. First Order Evolution Equations      Introduction      The Cauchy Problem      Generation of Semigroups      Accretive Operators; two examples      Generation of Groups; a wave equation      Analytic Semigroups      Parabolic EquationsV. Implicit Evolution Equations     Introduction     Regular Equations     Pseudoparabolic Equations     Degenerate Equations     ExamplesVI. Second Order Evolution Equations      Introduction      Regular Equations      Sobolev Equations      Degenerate Equations      ExamplesVII. 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   
  • 内容简介:
    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.
  • 目录:

                                     I. Elements of Hilbert Space   Linear Algebra   Convergence and Continuity   Completeness   Hilbert Space   Dual Operators; Identifications   Uniform Boundedness; Weak Compactness   Expansion in EigenfunctionsII. Distributions and Sobolev Spaces    Distributions    Sobolev Spaces    Trace    Sobolev's Lemma and Imbedding    Density and CompactnessIII. Boundary Value Problems      Introduction      Forms, Operators and Green's Formula      Abstract Boundary Value Problems      Examples      Coercivity; Elliptic Forms      Regularity      Closed operators, adjoints and eigenfunction expansionsIV. First Order Evolution Equations      Introduction      The Cauchy Problem      Generation of Semigroups      Accretive Operators; two examples      Generation of Groups; a wave equation      Analytic Semigroups      Parabolic EquationsV. Implicit Evolution Equations     Introduction     Regular Equations     Pseudoparabolic Equations     Degenerate Equations     ExamplesVI. Second Order Evolution Equations      Introduction      Regular Equations      Sobolev Equations      Degenerate Equations      ExamplesVII. 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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