Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models
著者
書誌事項
Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models
（Memoirs of the American Mathematical Society, no. 951）
American Mathematical Society, c2009
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注記
"Volume 202, number 951 (end of volume)."
Includes bibliographical references (p. 67-71)
内容説明・目次
内容説明
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.
目次
- Introduction
- Integrated semigroups
- Spectral decomposition of the state space
- Center manifold theory
- Hopf bifurcation in age structured models
- Bibliography.
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