Theory and Applications of Abstract Semilinear Cauchy Problems / Pierre Magal, Shigui Ruan.

Intro; Foreword; Preface; Contents; Acronyms; 1 Introduction; 1.1 Ordinary Differential Equations; 1.1.1 Spectral Properties of Matrices; 1.1.2 State Space Decomposition; 1.1.3 Semilinear Systems; 1.2 Retarded Functional Differential Equations; 1.2.1 Existence and Uniqueness of Solutions; 1.2.2 Linearized Equation at an Equilibrium; 1.2.3 Characteristic Equations; 1.2.4 Center Manifolds; 1.3 Age-Structured Models; 1.3.1 Volterra Formulation; 1.3.2 Age-Structured Models Without Birth; 1.3.3 Age-Structured Models with Birth; 1.3.4 Equilibria and Linearized Equations

1.3.5 Age-Structured Models Reduce to DDEs and ODEs1.4 Abstract Semilinear Formulation; 1.4.1 Functional Differential Equations; 1.4.2 Age-Structured Models; 1.4.3 Size-Structured Models; 1.4.4 Partial Functional Differential Equations; 1.5 Remarks and Notes; 2 Semigroups and Hille-Yosida Theorem; 2.1 Semigroups; 2.1.1 Bounded Case; 2.1.2 Unbounded Case; 2.2 Resolvents; 2.3 Infinitesimal Generators; 2.4 Hille-Yosida Theorem; 2.5 Nonhomogeneous Cauchy Problem; 2.6 Examples; 2.7 Remarks and Notes; 3 Integrated Semigroups and Cauchy Problems with Non-dense Domain; 3.1 Preliminaries

3.2 Integrated Semigroups3.3 Exponentially Bounded Integrated Semigroups; 3.4 Existence of Mild Solutions; 3.5 Bounded Perturbation; 3.6 The Hille-Yosida Case; 3.7 The Non-Hille-Yosida Case; 3.8 Applications to a Vector Valued Age-Structured Model in Lp; 3.9 Remarks and Notes; 4 Spectral Theory for Linear Operators; 4.1 Basic Properties of Analytic Maps; 4.2 Spectra and Resolvents of Linear Operators; 4.3 Spectral Theory of Bounded Linear Operators; 4.4 Essential Growth Bound of Linear Operators; 4.5 Spectral Decomposition of the State Space

4.6 Asynchronous Exponential Growth of Linear Operators4.7 Remarks and Notes; 5 Semilinear Cauchy Problems with Non-dense Domain; 5.1 Introduction; 5.2 Existence and Uniqueness of a Maximal Semiflow: The Blowup Condition; 5.3 Positivity; 5.4 Lipschitz Perturbation; 5.5 Differentiability with Respect to the State Variable; 5.6 Time Differentiability and Classical Solutions; 5.7 Stability of Equilibria; 5.8 Remarks and Notes; 6 Center Manifolds, Hopf Bifurcation, and Normal Forms; 6.1 Center Manifold Theory; 6.1.1 Existence of Center Manifolds; 6.1.2 Smoothness of Center Manifolds

6.2 Hopf Bifurcation6.2.1 State Space Decomposition; 6.2.2 Hopf Bifurcation Theorem; 6.3 Normal Form Theory; 6.3.1 Nonresonant Type Results; 6.3.2 Normal Form Computation; 6.4 Remarks and Notes; 7 Functional Differential Equations; 7.1 Retarded Functional Differential Equations; 7.1.1 Integrated Solutions and Spectral Analysis; 7.1.2 Projectors on the Eigenspaces; 7.1.3 Hopf Bifurcation; 7.2 Neutral Functional Differential Equations; 7.2.1 Spectral Theory; 7.2.2 Projectors on the Eigenspaces; 7.3 Partial Functional Differential Equations