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

Magal, Pierre author., Author,
1st ed. 2018.
Cham : Springer International Publishing : Imprint: Springer, 2018.
Mathematics and Statistics (Springer-11649)
Applied mathematical sciences (Springer-Verlag New York Inc.) 0066-5452 ; 201
Applied Mathematical Sciences, 0066-5452 ; 201
1 online resource (XXII, 543 pages) : 17 illustrations, 10 illustrations in color.
Differential equations.
Differential equations, Partial.
Local subjects:
Ordinary Differential Equations.
Partial Differential Equations.
System Details:
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Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.
Chapter 1- Introduction
Chapter 2- Semigroups and Hille-Yosida Theorem
Chapter 3- Integrated Semigroups and Cauchy Problems with Non-dense Domain
Chapter 4- Spectral Theory for Linear Operators
Chapter 5- Semilinear Cauchy Problems with Non-dense Domain
Chapter 6- Center Manifolds, Hopf Bifurcation and Normal Forms
Chapter 7- Functional Differential Equations
Chapter 8- Age-structured Models
Chapter 9- Parabolic Equations
Ruan, Shigui. author., Author,
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Publisher Number:
10.1007/978-3-030-01506-0 doi
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