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Titlebook: Evolutionary Integral Equations and Applications; Jan Prüss Book 2012 Springer Basel 2012 dynamical problems.electrodynamics with memory.i

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发表于 2025-3-21 18:35:06 | 显示全部楼层 |阅读模式
书目名称Evolutionary Integral Equations and Applications
编辑Jan Prüss
视频video
概述Presents a general approach to linear evolutionary systems.Clearly written and of lasting value.A substantial part of the results presented originate from the author?
丛书名称Modern Birkhäuser Classics
图书封面Titlebook: Evolutionary Integral Equations and Applications;  Jan Prüss Book 2012 Springer Basel 2012 dynamical problems.electrodynamics with memory.i
描述This book deals with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space. The main feature of the kernels involved is that they consist of unbounded linear operators. The aim is a coherent presentation of the state of art of the theory including detailed proofs and its applications to problems from mathematical physics, such as viscoelasticity, heat conduction, and electrodynamics with memory. The importance of evolutionary integral equations ‒ which form a larger class than do evolution equations​ ‒ stems from such applications and therefore special emphasis is placed on these. A number of models are derived and, by means of the developed theory, discussed thoroughly. An annotated bibliography containing 450 entries increases the book’s value as an incisive reference text.---This excellent book presents a general approach to linear evolutionary systems, with an emphasis on infinite-dimensional systems with time delays, such as those occurring in linear viscoelasticity with or without thermal effects. It gives a very natural and mature extension of the usual semigroup approach to a more general class of infinite-dimensional
出版日期Book 2012
关键词dynamical problems; electrodynamics with memory; integrodifferential equations; linear Volterra integra
版次1
doihttps://doi.org/10.1007/978-3-0348-0499-8
isbn_softcover978-3-0348-0498-1
isbn_ebook978-3-0348-0499-8Series ISSN 2197-1803 Series E-ISSN 2197-1811
issn_series 2197-1803
copyrightSpringer Basel 2012
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发表于 2025-3-21 23:03:28 | 显示全部楼层
Paul Kligfield MD,Peter M. Okin MD under perturbations as analytic resolvents. Again the maximal regularity property of type . is valid, even for the perturbed equation. In Section 3.6 we derive a representation formula for the resolvent in case . is the generator of a .0-semigroup.
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Theory of Repetitive Facilitative Exercised material functions shows that the notion of creep functions introduced in Section 4 appears here naturally. The well-posedness of some special problems which lead to Volterra equations of scalar type will be discussed, but also the limits of this class of equations become apparent.
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https://doi.org/10.1007/978-3-030-16818-6e analog of the Hille-Yosida theorem of semigroup theory for Volterra equations, proved in Section 1.5, is of fundamental importance in later chapters. The theory is completed with several counterexamples, and with a discussion of the integral resolvent.
发表于 2025-3-22 22:41:42 | 显示全部楼层
Legal Aspects of Graded Exercise Testingy of analytic resolvents is studied and a characterization of analytic semigroups in these terms is derived. It is shown that analytic resolvents lead to improved perturbation results and stronger properties of the variation of parameter formulas.
发表于 2025-3-23 01:51:28 | 显示全部楼层
Physical training in coronary heart disease,explicitly represented in terms of the given one, and of the propagation function associated with a completely positive kernel. This representation is particularly useful for the understanding of the regularity and the asymptotic behaviour of the resolvent.
发表于 2025-3-23 05:38:14 | 显示全部楼层
Resolventse analog of the Hille-Yosida theorem of semigroup theory for Volterra equations, proved in Section 1.5, is of fundamental importance in later chapters. The theory is completed with several counterexamples, and with a discussion of the integral resolvent.
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