Infinite Dimensional Dynamical Systems

1. Front Matter

   Pages i-viii

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2. Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems

   • Jack K. Hale, Geneviève Raugel

   Pages 1-55

3. Spectral Theory for Forward Nonautonomous Parabolic Equations and Applications

   • Janusz Mierczyński, Wenxian Shen

   Pages 57-99

4. A Dynamical Systems Approach to Traveling Wave Solutions for Liquid/Vapor Phase Transition

   • Haitao Fan, Xiao-Biao Lin

   Pages 101-117

5. Instability of Radially-Symmetric Spikes in Systems with a Conserved Quantity

   • Alin Pogan, Arnd Scheel

   Pages 119-140

6. Global Hopf Bifurcation Analysis of a Neuron Network Model with Time Delays

   • Michael Y. Li, Junjie Wei

   Pages 141-168

7. Instability of Low Density Supersonic Waves of a Viscous Isentropic Gas Flow Through a Nozzle

   • Weishi Liu, Myunghyun Oh

   Pages 169-183

8. A Simple Proof of the Stability of Solitary Waves in the Fermi-Pasta-Ulam Model Near the KdV Limit

   • A. Hoffman, C. Eugene Wayne

   Pages 185-192

9. Littlewood Problem for a Singular Subquadratic Potential

   • Xiong Li, Yingfei Yi

   Pages 193-209

10. Semiflows for Neutral Equations with State-Dependent Delays

    • Hans-Otto Walther

    Pages 211-267

11. Threshold Dynamics of Scalar Linear Periodic Delay-Differential Equations

    • Yuming Chen, Jianhong Wu

    Pages 269-278

12. Differential Equations with Random Delay

    • S. Siegmund, T. S. Doan

    Pages 279-303

13. Beyond Diffusion: Conditional Dispersal in Ecological Models

    • Chris Cosner

    Pages 305-317

14. Global Attractor of a Coupled Two-Cell Brusselator Model

    • Yuncheng You

    Pages 319-352

15. Projectors on the Generalized Eigenspaces for Partial Differential Equations with Time Delay

    • Arnaut Ducrot, Pierre Magal, Shigui Ruan

    Pages 353-390

16. Global Convergence in Monotone and Uniformly Stable Recurrent Skew-Product Semiflows

    • Yejuan Wang, Xiao-Qiang Zhao

    Pages 391-406

17. The Infinite Hierarchy of Elastic Shell Models: Some Recent Results and a Conjecture

    • Marta Lewicka, Mohammad Reza Pakzad

    Pages 407-420

18. Traveling Wavefronts in Lattice Differential Equations with Time Delay and Global Interaction

    • Shiwang Ma, Xingfu Zou

    Pages 421-443

19. Bifurcation of Limit Cycles from a Non-Hamiltonian Quadratic Integrable System with Homoclinic Loop

    • Yulin Zhao, Huaiping Zhu

    Pages 445-479

20. Anomalous Diffusion in Polymers: Long-Time Behaviour

    • Dmitry A. Vorotnikov

    Pages 481-496

​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.​ 

• hyperbolic partial differential equations
• infinite dimensional dynamical systems
• non-autonomous dynamical systems
• parabolic partial differential equations
• skew-product flows
• stochastic differential equations
• partial differential equations
• ordinary differential equations

• Division of Applied Mathematics, Brown University, Providence, USA

  John Mallet-Paret

• Department of Mathematics and Statistics, York University, Toronto, Canada

  Jianhong Wu, Huaiping Zhu

• Georgia Institute of Technology, School of Mathematics, Atlanta, USA

  Yingfei Yi

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