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This collection covers a wide range of topics of infinitedimensional dynamical systems generated by parabolic partial differentialequations, hyperbolic partial differential equations, solitary equations,lattice differential equations, delay differential equations, and stochasticdifferential equations.Infinite dimensional dynamical systems are generated byevolutionary equations describing the evolutions in time of systems whosestatus must be depicted in infinite dimensional phase spaces. Studying thelong-term behaviors of such systems is important in our understanding of theirspatiotemporal pattern formation and global continuation, and has been amongmajor sources of motivation and applications of new developments of nonlinearanalysis and other mathematical theories. Theories of the infinite dimensionaldynamical systems have also found more and more important applications inphysical, chemical, and life sciences.This book collects 19 papers from 48 invited lecturers tothe International Conference on Infinite Dimensional Dynamical Systems held atYork University, Toronto, in September of 2008. As the conference was dedicatedto Professor George Sell from University of Minnesota on the occasion of his70th birthday, this collection reflects the pioneering work and influence ofProfessor Sell in a few core areas of dynamical systems, includingnon-autonomous dynamical systems, skew-product flows, invariant manifoldstheory, infinite dimensional dynamicalsystems, approximation dynamics, and fluid flows.
List of contents
Preface.- Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems (J. Hale, G. Raugel).- Spectral Theory for Forward Nonautonomus Parabolic Equations and Applications (J. Mierczynski, W. Shen).- A Dynamical Systems Approach to Traveling Wave Solutions for Liquid/Vapor Phase Transition (H. Fan, X. Lin).- Instability of Radially-Symmetric Spikes in Systems with Conserved Quantity (A. Pogan, A. Scheel).- Global Hopf Bifurcation Analysis of a Neuron Network Model with Time Delays (M. Li, J. Wei).- Instability of Low Density Supersonic Waves of a Viscous Isentropic Gas Flow Through a Nozel (W. Liu, M. Oh).- A Simple Proof of the Stability of Solitary Waves in the Fermi-Pasta-Ulam Model Near the KdV Limit (A. Hoffman, G. Wayne).- Littlewood Problem for a Singular Subquadratic Potential (X. Li, Y. Yi).- Semiflows for Neutral Equations with State-dependent Delay (H.-O. Walther).- Threshold Dynamics of Scalar Linear Periodic Delay-Differential Equations (Y. Chen, J. Wu).- Differential Equations with Random Delay (T.S. Doan, S. Siegmund).- Beyond Diffusion: Conditional Dispersal in Ecological Models (C. Cosner).- Global Attractor of a Coupled Two-Cell Brusselator Model (Y. You).- Projectors on the Generalized Eigenspaces for Partial Differential Equations with Time Delay (A. Ducrot, P. Magal, S. Ruan).- Global Convergence in Monotone and Uniformly Stable Recurrent Skew-Product Semiflows (Y. Wang, X. Zhao).- The Infinite Hierarchy of Elastic Shell Models: Some Recent Results and a Conjecture (M. Lewicka, R. Pakzad).- Traveling Wavefronts for Lattic Differential Equations with Time Delay and Global Interaction (S. Ma, Z. Zou).- Bifurcation of Limit Cycles from a Non-Hamiltonian Quadratic Integrable System with Homoclinic Loop (Y. Zhao, H. Zhu) Anomalous Diffusion in Polymers: Long-Time Behaviour (D. Vorotnikov).
Summary
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.
