Theory and Applications of Abstract Semilinear Cauchy Problems. 1st ed. 2018

種類:

電子ブック

責任表示:

by Pierre Magal, Shigui Ruan

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Magal, Pierre.
• Ruan, Shigui.
• SpringerLink (Online service)

シリーズ名:

Applied Mathematical Sciences ; 201

ISBN:

9783030015060 [3030015068]    

注記:

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 -- References -- Index.
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

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