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Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models
Pierre MagalShigui Ruan
出版American Mathematical Soc., 2009
主題Mathematics / Differential Equations / GeneralMathematics / Differential Equations / Partial
ISBN08218465319780821846537
URLhttp://books.google.com.hk/books?id=C7uIAwAAQBAJ&hl=&source=gbs_api
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註釋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.