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Titlebook: Distribution Theory Applied to Differential Equations; Adina Chirilă,Marin Marin,Andreas Öchsner Book 2021 The Editor(s) (if applicable) a

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发表于 2025-3-21 16:34:05 | 显示全部楼层 |阅读模式
书目名称Distribution Theory Applied to Differential Equations
编辑Adina Chirilă,Marin Marin,Andreas Öchsner
视频video
概述Presents important contributions to modern theories concerning the distribution theory applied to convex analysis.Includes approximate formulations of variation problems, such as the Galerkin method o
图书封面Titlebook: Distribution Theory Applied to Differential Equations;  Adina Chirilă,Marin Marin,Andreas Öchsner Book 2021 The Editor(s) (if applicable) a
描述.This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function). The authors prove several basic results in distribution theory and present ordinary differential equations and partial differential equations by providing generalized solutions. In addition, the book deals with Sobolev spaces, which presents aspects related to variation problems, such as the Stokes system, the elasticity system and the plate equation. The authors also include approximate formulations of variation problems, such as the Galerkin method or the finite element method. ..The book is accessible to all scientists, and it is especially useful for those who use mathematics to solve engineering and physics problems. The authors have avoided concepts and results contained in other books in order to keep the book comprehensive. Furthermore, they do not present concrete simplified models and pay maximal attention to scientific rigor..
出版日期Book 2021
关键词Sobolev Space; Variational Formulation; Tempered Distributions; Subdifferential; Evolution Equations; Dif
版次1
doihttps://doi.org/10.1007/978-3-030-67159-4
isbn_softcover978-3-030-67161-7
isbn_ebook978-3-030-67159-4
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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发表于 2025-3-21 22:12:15 | 显示全部楼层
The Subdifferential of a Convex Function,t of subdifferentiability. Monotone and maximal monotone operators are defined. Minty’s theorem is proved. The subdifferential is shown to be a maximal monotone operator. The conjugate function is used to transform a minimization problem into a maximization problem and conversely. Finally, the addit
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Differential Equations in Distributions,discussed in the framework of the theory of distributions. Hyperbolic, parabolic and elliptic partial differential equations are solved by means of the Fourier transform. The Cauchy problem is discussed.
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Variational Problems,l formulations of the Stokes system, the elasticity system and the plate equation. Then we discuss the approximation of variational problems by means of the Galerkin method and by means of the finite element method.
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