| 書目名稱 | Theory and Applications of Abstract Semilinear Cauchy Problems | | 編輯 | Pierre Magal,Shigui Ruan | | 視頻video | http://file.papertrans.cn/924/923542/923542.mp4 | | 概述 | Allows readers and graduate students with no background to start with the basic concepts.The application-oriented readers will see how the abstract results apply to biological and physical problems.Le | | 叢書名稱 | Applied Mathematical Sciences | | 圖書封面 |  | | 描述 | 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 manifoldtheory, 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, an | | 出版日期 | Book 2018 | | 關(guān)鍵詞 | abstract semilinear cauchy problems; densely and non-densely defined cauchy problems; integrated semig | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-01506-0 | | isbn_ebook | 978-3-030-01506-0Series ISSN 0066-5452 Series E-ISSN 2196-968X | | issn_series | 0066-5452 | | copyright | Springer Nature Switzerland AG 2018 |
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