Description

Book Synopsis
Introduces methods in the theory of partial differential equations derivable from a Lagrangian. This book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E Noether.

Table of Contents
General Introduction 3 1 1.0 Introduction 7 1.1 The Lagrangian Picture 8 1.2 The Hamiltonian Picture 19 1.3 Examples 28 2 2.0 Introduction 51 2.1 The Canonlicd and Symplectic Forms 57 2.2 Symplectic Transformations 62 2.3 The Equations of Variation 79 2.4 The Circulation Theorem 84 2.5 The Euler System 87 2.6 Irrotational Solutions 96 2.7 The Equation of Continuity 99 3 3.0 Introduction 105 3.1 Compatible Currents 108 3.2 Null Currents and Null Lagragians 125 3.3 The Source Equations 128 3.4 The Generic Case n > 1 & m > 2 133 3.5 The Separable Case m > 2 141 3.6 The Case m = 2 144 3.7 Lie Flows and the Noether Current 146 4 4.1 Sections of Vector Bundles 159 5 5.0 Introduction 191 5.1 Relative Lagrangians 195 5.2 Ellipticity and Hyperbolicity 220 5.3 The Domain of Dependence 240 6 6.1 The Electromagnetic Field 263 6.2 Electromagnetic Symplectic Structure 272 6.3 Electromagnetic Compatible Currents 282 6.4 Causality in Electromagnetic etic Theory 299 Bibliography 315 Index 317

The Action Principle and Partial Differential

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    A Paperback / softback by Demetrios Christodoulou

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      Book details

      Publisher Princeton University Press
      Published 17 January 2000
      ISBN-13 9780691049571
      978-0691049571
      ISBN-10 0691049572
      Also in:
      Mathematics

      Description

      Book Synopsis
      Introduces methods in the theory of partial differential equations derivable from a Lagrangian. This book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E Noether.

      Table of Contents
      General Introduction 3 1 1.0 Introduction 7 1.1 The Lagrangian Picture 8 1.2 The Hamiltonian Picture 19 1.3 Examples 28 2 2.0 Introduction 51 2.1 The Canonlicd and Symplectic Forms 57 2.2 Symplectic Transformations 62 2.3 The Equations of Variation 79 2.4 The Circulation Theorem 84 2.5 The Euler System 87 2.6 Irrotational Solutions 96 2.7 The Equation of Continuity 99 3 3.0 Introduction 105 3.1 Compatible Currents 108 3.2 Null Currents and Null Lagragians 125 3.3 The Source Equations 128 3.4 The Generic Case n > 1 & m > 2 133 3.5 The Separable Case m > 2 141 3.6 The Case m = 2 144 3.7 Lie Flows and the Noether Current 146 4 4.1 Sections of Vector Bundles 159 5 5.0 Introduction 191 5.1 Relative Lagrangians 195 5.2 Ellipticity and Hyperbolicity 220 5.3 The Domain of Dependence 240 6 6.1 The Electromagnetic Field 263 6.2 Electromagnetic Symplectic Structure 272 6.3 Electromagnetic Compatible Currents 282 6.4 Causality in Electromagnetic etic Theory 299 Bibliography 315 Index 317

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