PDE dynamics : an introduction
Author(s)
Bibliographic Information
PDE dynamics : an introduction
(Mathematical modeling and computation, 23)
Society for Industrial and Applied Mathematics, c2019
- : pbk
Available at 5 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references (p. 211-240) and index
Description and Table of Contents
Description
This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research.
PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.
Table of Contents
- Preface
- Course Design
- 1 A Whirlwind Introduction
- 2 Some ODE Theory and Geometric Dynamics
- 3 Some PDE Theory and Functional Analysis
- 4 Implicit Functions and Lyapunov-Schmidt
- 5 Crandall-Rabinowitz and Local Bifurcations
- 6 Stability and Spectral Theory
- 7 Existence of Travelling Waves
- 8 Pushed and Pulled Fronts
- 9 Sturm-Liouville and Stability of Travelling Waves
- 10 Exponential Dichotomies and Evans Function
- 11 Characteristics and Shocks
- 12 Onset of Patterns and Multiple Scales
- 13 Validity of Amplitude Equations
- 14 Semigroups and Sectorial Operators
- 15 Dissipation and Absorbing Sets
- 16 Nonlinear Saddles and Invariant Manifolds
- 17 Spectral Gap and Inertial Manifolds
- 18 Attractors and the Variational Equation
- 19 Lyapunov Exponents and Fractal Dimension
- 20 Metastability and Manifolds
- 21 Exponentially Small Terms
- 22 Coarsening Bounds and Scaling
- 23 Gradient Flows and Lyapunov Functions
- 24 Entropies and Global Decay
- 25 Convexity and Minimizers
- 26 Mountain Passes and Periodic Waves
- 27 Hamiltonian Dynamics and Normal Forms
- 28 Empirical Measures and the Mean Field
- 29 Two Effects: Hypocoercivity and Turing
- 30 Blow-up in Cross-Diffusion Systems
- 31 Self-Similarity and Free Boundaries
- 32 Spirals and Symmetry
- 33 Averaging and Ergodicity
- 34 Two-Scale Convergence
- 35 Asymptotics and Layers
- 36 Fast-Slow Systems: Periodicity and Chaos
- A Finite Differences and Simulation
- B Finite Elements and Continuation
- Bibliography
- Index.
by "Nielsen BookData"