## Infinite Dimensional Dynamical SystemsJohn Mallet-Paret, Jianhong Wu, Yingfei Yi, Huaiping Zhu 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

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 |

481 | |

Semiflows for Neutral Equations with StateDependent Delays | 210 |

Threshold Dynamics of Scalar Linear Periodic DelayDifferentialEquations | 269 |

Differential Equations with Random Delay | 279 |

### Other editions - View all

Infinite Dimensional Dynamical Systems John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi Limited preview - 2012 |

Infinite Dimensional Dynamical Systems John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi No preview available - 2014 |

Infinite Dimensional Dynamical Systems John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi No preview available - 2012 |

### Common terms and phrases

Abelian integrals absorbing set Amax(a Amin(a assume assumption asymptotically Banach space boundary conditions bounded bounded linear operator Co(X compact consider continuously differentiable converges Corollary defined definition delay denote domain dynamical systems eigenvalue equilibrium essential spectrum estimate exists exponential fixed point follows functional differential equations given global attractor hence Hopf bifurcation Hypothesis implies inequality integral Lemma limsup linear operator Lipschitz continuous Lyapunov exponents Math Mathematics Mathematics Subject Classification minimal monotone Moreover nonlinear norm obtain parabolic equations periodic solution perturbation positive constant principal spectrum problem properties Proposition prove random dynamical system reaction-diffusion resp respect result satisfies Sect semigroup sequence skew-product semiflow Springer Science+Business Media stable subset Theorem 1.1 theory topology traveling wave uniformly unique unstable weak solutions Yo(a