Variational Techniques for Elliptic Partial Differential Equations: Theoretical Tools and Advanced Applications
暫譯: 橢圓偏微分方程的變分技術：理論工具與進階應用
Sayas, Francisco J., Brown, Thomas S., Hassell, Matthew E.
- 出版商: CRC
- 出版日期: 2019-01-25
- 售價: $4,110
- 貴賓價: 9.5 折 $3,905
- 語言: 英文
- 頁數: 514
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1138580880
- ISBN-13: 9781138580886
海外代購書籍(需單獨結帳)
商品描述
Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and theorems from distribution theory, the book gradually builds the functional analytic framework for studying elliptic PDE using variational formulations. Rather than introducing all of the prerequisites in the first chapters, it is the introduction of new problems which motivates the development of the associated analytical tools. In this way the student who is encountering this material for the first time will be aware of exactly what theory is needed, and for which problems.
Features
- A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields
- An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two
- Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc.
- A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics
商品描述(中文翻譯)
《變分技術於橢圓偏微分方程》，旨在為研究應用數學、分析及/或數值分析的研究生提供必要的工具，以理解橢圓偏微分方程的結構和可解性。本書從分佈理論的必要定義和定理開始，逐步建立使用變分形式研究橢圓 PDE 的函數分析框架。與其在前幾章介紹所有的先決條件，不如通過引入新問題來激發相關分析工具的發展。這樣，第一次接觸這些材料的學生將清楚地知道需要哪些理論，以及針對哪些問題。
特點
- 對於 Lipschitz 領域上 Sobolev 空間理論的詳細且嚴謹的發展，包括跡運算子和向量場的法向分量
- 將涉及希爾伯特空間的函數分析概念進行整合，並解決這些概念所能解決的問題，而不是將兩者分開
- 介紹解決物理問題所需的分析工具，如時間諧波波、斯托克斯流和達西流、表面微分方程、麥克斯韋腔問題等
- 提供各種問題以加強和擴展每章的材料，包括流體和固體力學的應用
作者簡介
Francisco-Javier Sayas is a Professor of Mathematical Sciences at the University of Delaware. He has published over one hundred research articles in refereed journals, and is the author of Retarded Potentials and Time Domain Boundary Integral Equations.
Thomas S. Brown is a lecturer in Computational and Applied Mathematics at Rice University. He received his PhD in Mathematics from the University of Delaware in 2018, under the supervision of Francisco-Javier Sayas. His expertise lies in the theoretical and numerical study of elastic wave propagation in piezoelectric media with applications to control problems.
Matthew E. Hassell is a Systems Engineer at Lockheed Martin. He received his PhD in Applied Mathematics from the University of Delaware in 2016, under the supervision of Francisco-Javier Sayas, working on convolution quadrature techniques for problems in wave propagation and scattering by non-homogeneous media as well as viscous flow around obstacles.
作者簡介(中文翻譯)
Francisco-Javier Sayas 是德拉瓦大學的數學科學教授。他在經過審核的期刊上發表了超過一百篇研究文章，並且是 Retarded Potentials and Time Domain Boundary Integral Equations 的作者。
Thomas S. Brown 是萊斯大學計算與應用數學的講師。他於2018年在德拉瓦大學獲得數學博士學位，指導教授為 Francisco-Javier Sayas。他的專長在於對壓電介質中彈性波傳播的理論與數值研究，並應用於控制問題。
Matthew E. Hassell 是洛克希德·馬丁公司的系統工程師。他於2016年在德拉瓦大學獲得應用數學博士學位，指導教授為 Francisco-Javier Sayas，研究主題為針對非均質介質的波傳播與散射問題的卷積求積技術，以及圍繞障礙物的粘性流動。
