| 书目名称 | Existence Families, Functional Calculi and Evolution Equations | | 编辑 | Ralph deLaubenfels | | 视频video | | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as ‘existent families‘ and ‘regularized semigroups‘. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, organized way, together with a great deal of new material. | | 出版日期 | Book 1994 | | 关键词 | Semigroups of operators; abstract Cauchy problem; calculus; evolution equations; functional calculus; max | | 版次 | 1 | | doi | https://doi.org/10.1007/BFb0073401 | | isbn_softcover | 978-3-540-57703-4 | | isbn_ebook | 978-3-540-48322-9Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 1994 |
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