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Titlebook: Hyperbolic Functional Differential Inequalities and Applications; Zdzislaw Kamont Book 1999 Springer Science+Business Media Dordrecht 1999

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发表于 2025-3-21 17:45:44 | 显示全部楼层 |阅读模式
书目名称Hyperbolic Functional Differential Inequalities and Applications
编辑Zdzislaw Kamont
视频videohttp://file.papertrans.cn/431/430590/430590.mp4
丛书名称Mathematics and Its Applications
图书封面Titlebook: Hyperbolic Functional Differential Inequalities and Applications;  Zdzislaw Kamont Book 1999 Springer Science+Business Media Dordrecht 1999
描述This book is intended as a self-contained exposition of hyperbolic functional dif­ ferential inequalities and their applications. Its aim is to give a systematic and unified presentation of recent developments of the following problems: (i) functional differential inequalities generated by initial and mixed problems, (ii) existence theory of local and global solutions, (iii) functional integral equations generated by hyperbolic equations, (iv) numerical method of lines for hyperbolic problems, (v) difference methods for initial and initial-boundary value problems. Beside classical solutions, the following classes of weak solutions are treated: Ca­ ratheodory solutions for quasilinear equations, entropy solutions and viscosity so­ lutions for nonlinear problems and solutions in the Friedrichs sense for almost linear equations. The theory of difference and differential difference equations ge­ nerated by original problems is discussed and its applications to the constructions of numerical methods for functional differential problems are presented. The monograph is intended for different groups of scientists. Pure mathemati­ cians and graduate students will find an advanced theory of
出版日期Book 1999
关键词Approximation; Boundary value problem; Cauchy problem; DEX; Volume; algorithms; boundary element method; de
版次1
doihttps://doi.org/10.1007/978-94-011-4635-7
isbn_softcover978-94-010-5957-2
isbn_ebook978-94-011-4635-7
copyrightSpringer Science+Business Media Dordrecht 1999
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发表于 2025-3-21 20:24:00 | 显示全部楼层
发表于 2025-3-22 04:09:52 | 显示全部楼层
Numerical Method of Lines, is studied in [91]. The book [189] demonstrates lots of examples of the use of the numerical method of lines. Convergence analysis of one step difference methods generated by the numerical method of lines was investigated in [186].
发表于 2025-3-22 08:22:19 | 显示全部楼层
Generalized Solutions,l problems can be found in [42, 107, 123]. Distributional solutions of almost linear problems were considered in [204]. The method used in this paper is constructive, it is based on a difference scheme. Barbashin type functional differential problems are discussed in [102].
发表于 2025-3-22 11:09:36 | 显示全部楼层
Functional Integral Equations,sional set. Let ..(..(.)) denotes the .. — dimensional Lebesgue measure of ..(.). We assume that .. does not depend on .. If the .. — dimensional hyperplane containing the set ..(.) and being parallel to the coordinate axes is defined by the equations.then.denotes the .. dimensional Lebesgue integral in the space.and ..
发表于 2025-3-22 15:31:09 | 显示全部楼层
Initial Problems on the Haar Pyramid,. In particular, uniqueness results for initial problems on the Haar pyramid with nonlinear a priori estimates, were obtained as consequences of suitable comparison theorems for differential inequalities. The authors deal with solutions which admit first order partial derivatives and are totally dif
发表于 2025-3-22 20:20:00 | 显示全部楼层
Existence of Solutions on the Haar Pyramid,Write..=[−.., 0] × [−., .] where .. ∈ .., Ω = . × .(.. ∪ ., .) × ..and.Suppose that .: Ω → . and .: .. → . are given functions. Consider the Cauchy problem.where ... = (....,…, ...). In this Chapter we consider classical solutions of problem (2.1), (2.2). We assume that the operator . satisfies the
发表于 2025-3-23 00:48:06 | 显示全部楼层
Numerical Method of Lines,is transformed into a system of ordinary differential equations. The method is used for approximation of solutions of nonlinear differential problems of parabolic type by solutions of ordinary equations ([91, 153, 219, 220, 222, 225, 238]). The method is also treated as a tool for proving of existen
发表于 2025-3-23 04:18:39 | 显示全部楼层
Generalized Solutions,systems in two independent variables were considered in [167], see also [102]. A continuous function is a solution of a mixed problem if it satisfies integral functional system arising from functional differential system by integrating along bicharacteristics. The paper [167] initiated investigation
发表于 2025-3-23 07:52:43 | 显示全部楼层
Functional Integral Equations,ts of the space .. will be denoted by . = (.., …, ..), . = (.., …, ..). Let . ⊂ . be a compact set and .(.) = }ξ ∈ .:ξ≤.}. Assume that functions.are given and β(.) ≤ ., α.(.) ≤ ., 1 ≤ . ≤ ., for . ∈ .. Suppose that the sets ..(.) ⊂ .(.) for . ∈ ., 1 ≤ . ≤ ., are given. We assume further that ..(.) i
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