Infinite Dimensional Dynamical Systems

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John Mallet-Paret, Jianhong Wu, Yingfei Yi, Huaiping Zhu
Springer Science & Business Media, Oct 11, 2012 - Mathematics - 496 pages
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.
 

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Contents

Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems
1
Spectral Theory for Forward Nonautonomous Parabolic Equations and Applications
56
A Dynamical Systems Approach to Traveling Wave Solutions for LiquidVapor Phase Transition
101
Instability of RadiallySymmetric Spikes in Systemswith a Conserved Quantity
118
Global Hopf Bifurcation Analysis of a Neuron Network Model with Time Delays
141
Instability of Low Density Supersonic Waves of a Viscous Isentropic Gas Flow Through a Nozzle
169
A Simple Proof of the Stability of Solitary Wavesin the FermiPastaUlam Model Near the KdV Limit
185
Littlewood Problem for a Singular Subquadratic Potential
193
Conditional Dispersal in Ecological Models
304
Global Attractor of a Coupled TwoCell Brusselator Model
319
Projectors on the Generalized Eigenspaces for Partial Differential Equations with Time Delay
353
Global Convergence in Monotone and Uniformly Stable Recurrent SkewProduct Semiflows
391
Some Recent Results and a Conjecture
407
Traveling Wavefronts in Lattice Differential Equations with TimeDelay and Global Interaction
421
Bifurcation of Limit Cycles from a NonHamiltonian Quadratic Integrable System with Homoclinic Loop
444
LongTime Behaviour
481

Semiflows for Neutral Equations with StateDependent Delays
210
Threshold Dynamics of Scalar Linear Periodic DelayDifferentialEquations
269
Differential Equations with Random Delay
279

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