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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
Shigui Ruan University of Miami, Coral Gables, FL
Available Formats:
Electronic ISBN: 978-1-4704-0565-6
Product Code: MEMO/202/951.E
List Price: $66.00 MAA Member Price:$59.40
AMS Member Price: $39.60 Click above image for expanded view 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 Shigui Ruan University of Miami, Coral Gables, FL Available Formats:  Electronic ISBN: 978-1-4704-0565-6 Product Code: MEMO/202/951.E  List Price:$66.00 MAA Member Price: $59.40 AMS Member Price:$39.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 2022009; 71 pp
MSC: Primary 35; 92;

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.

• Chapters
• 1. Introduction
• 2. Integrated Semigroups
• 3. Spectral Decomposition of the State Space
• 4. Center Manifold Theory
• 5. Hopf Bifurcation in Age Structured Models
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Volume: 2022009; 71 pp
MSC: Primary 35; 92;

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.

• Chapters
• 1. Introduction
• 2. Integrated Semigroups
• 3. Spectral Decomposition of the State Space
• 4. Center Manifold Theory
• 5. Hopf Bifurcation in Age Structured Models
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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