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Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models
Pierre Magal, Université du Havre, Le Lavre, France, and Shigui Ruan, University of Miami, Coral Gables, FL
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Memoirs of the American Mathematical Society
2009; 71 pp; softcover
Volume: 202
ISBN-10: 0-8218-4653-1
ISBN-13: 978-0-8218-4653-7
List Price: US$62
Individual Members: US$37.20
Institutional Members: US$49.60
Order Code: MEMO/202/951
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Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.

Table of Contents

  • Introduction
  • Integrated semigroups
  • Spectral decomposition of the state space
  • Center manifold theory
  • Hopf bifurcation in age structured models
  • Bibliography
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