Infinite Dimensional Dynamical Systems

✍ Scribed by Jack K. Hale, Geneviève Raugel (auth.), John Mallet-Paret, Jianhong Wu, Yingfie Yi, Huaiping Zhu (eds.)

• Publisher: Springer-Verlag New York
• Year: 2013
• Tongue: English
• Leaves: 494
• Series: Fields Institute Communications 64
• Edition: 1
• Category: Library

✦ Synopsis

​This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.​

✦ Table of Contents

Front Matter....Pages i-viii
Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems....Pages 1-55
Spectral Theory for Forward Nonautonomous Parabolic Equations and Applications....Pages 57-99
A Dynamical Systems Approach to Traveling Wave Solutions for Liquid/Vapor Phase Transition....Pages 101-117
Instability of Radially-Symmetric Spikes in Systems with a Conserved Quantity....Pages 119-140
Global Hopf Bifurcation Analysis of a Neuron Network Model with Time Delays....Pages 141-168
Instability of Low Density Supersonic Waves of a Viscous Isentropic Gas Flow Through a Nozzle....Pages 169-183
A Simple Proof of the Stability of Solitary Waves in the Fermi-Pasta-Ulam Model Near the KdV Limit....Pages 185-192
Littlewood Problem for a Singular Subquadratic Potential....Pages 193-209
Semiflows for Neutral Equations with State-Dependent Delays....Pages 211-267
Threshold Dynamics of Scalar Linear Periodic Delay-Differential Equations....Pages 269-278
Differential Equations with Random Delay....Pages 279-303
Beyond Diffusion: Conditional Dispersal in Ecological Models....Pages 305-317
Global Attractor of a Coupled Two-Cell Brusselator Model....Pages 319-352
Projectors on the Generalized Eigenspaces for Partial Differential Equations with Time Delay....Pages 353-390
Global Convergence in Monotone and Uniformly Stable Recurrent Skew-Product Semiflows....Pages 391-406
The Infinite Hierarchy of Elastic Shell Models: Some Recent Results and a Conjecture....Pages 407-420
Traveling Wavefronts in Lattice Differential Equations with Time Delay and Global Interaction....Pages 421-443
Bifurcation of Limit Cycles from a Non-Hamiltonian Quadratic Integrable System with Homoclinic Loop....Pages 445-479
Anomalous Diffusion in Polymers: Long-Time Behaviour....Pages 481-496

✦ Subjects

Dynamical Systems and Ergodic Theory; Partial Differential Equations; Ordinary Differential Equations