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Evolution Semigroups in Dynamical Systems and Differential Equations
Introduction Semigroups on Banach spaces and evolution semigroups Evolution families and Howland semigroups Characterizations of dichotomy for evolution families Two applications of evolutionExpand
Center Manifolds for Infinite Dimensional Nonautonomous Differential Equations
Abstract We study a nonlinear integral equation for a center manifold of a semilinear nonautonomous differential equation having mild solutions. We assume that the linear part of the equation admits,Expand
Exponential Dichotomy and Mild Solutions of Nonautonomous Equations in Banach Spaces
We prove that the exponential dichotomy of a strongly continuous evolution family on a Banach space is equivalent to the existence and uniqueness of continuous bounded mild solutions of theExpand
Limits of quantum graph operators with shrinking edges
Abstract We address the question of convergence of Schrodinger operators on metric graphs with general self-adjoint vertex conditions as lengths of some of graph's edges shrink to zero. We determineExpand
A Spectral Mapping Theorem and Invariant Manifolds for Nonlinear Schr
A spectral mapping theorem is proved that resolves a key problem in applying invariant manifold the- orems to nonlinear Schr- odinger type equations. The theo- rem is applied to the operator thatExpand
The Essential Spectrum of the Linearized 2D Euler Operator is a Vertical Band
We prove that the essential spectrum of the operator obtained by linearization about a steady state of the Euler equations governing the motion of inviscid ideal fluid in dimension two is a verticalExpand
Stability of Traveling Waves for a Class of Reaction-Diffusion Systems That Arise in Chemical Reaction Models
Perturbations of the wave in $H^1$ or $BUC$ that are small in both the weighted norm and the un Weighted norm are shown to stay small in the unweighted norm and to decay exponentially to a shift of the traveling wave in the weightednorm. Expand
Evolution Semigroups, Translation Algebras, and Exponential Dichotomy of Cocycles☆
Abstract We study the exponential dichotomy of an exponentially bounded, strongly continuous cocycle over a continuous flow on a locally compact metric space Θ acting on a Banach space X . Our mainExpand
Stability Radius and Internal Versus External Stability in Banach Spaces: An Evolution Semigroup Approach
In this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems. These include autonomous and nonautonomousExpand
Hyperbolicity of semigroups and Fourier multipliers
We present a characterization of hyperbolicity for strongly continuous semigroups on Banach spaces in terms of Fourier multiplier properties of the resolvent of the generator. Hyperbolicity withExpand