Shock Waves and Reaction—Diffusion Equations

Shock Waves and Reaction—Diffusion Equations by Joel Smoller.

. . . the progress of physics will to a large extent depend on the progress of nonlinear mathe­ matics, of methods to solve nonlinear equations . . . and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wante...

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Bibliographic Details
Main Author: Smoller, Joel (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1983.
Edition:1st ed. 1983.
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 258
Springer eBook Collection.
Subjects:
Mathematical physics.
Acoustics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I Basic Linear Theory
  • 1 Ill-Posed Problems
  • 2 Characteristics and Initial-Value Problems
  • 3 The One-Dimensional Wave Equation
  • 4 Uniqueness and Energy Integrals
  • 5 Holmgren’s Uniqueness Theorem
  • 6 An Initial-Value Problem for a Hyperbolic Equation
  • 7 Distribution Theory
  • 8 Second-Order Linear Elliptic Equations
  • 9 Second-Order Linear Parabolic Equations
  • II Reaction—Diffusion Equations
  • 10 Comparison Theorems and Monotonicity Methods
  • 11 Linearization
  • 12 Topological Methods
  • 13 Bifurcation Theory
  • 14 Systems of Reaction—Diffusion Equations
  • III The Theory of Shock Waves
  • 15 Discontinuous Solutions of Conservation Laws
  • 16 The Single Conservation Law
  • 17 The Riemann Problem for Systems of Conservation Laws
  • 18 Applications to Gas Dynamics
  • 19 The Glimm Difference Scheme
  • 20 Riemann Invariants, Entropy, and Uniqueness
  • 21 Quasi-Linear Parabolic Systems
  • IV The Conley Index
  • 22 The Conley Index
  • 23 Index Pairs and the Continuation Theorem
  • 24 Travelling Waves
  • Author Index.

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