Analytic Methods for Coagulation-Fragmentation Models, Volume I
暫譯: 凝聚-碎裂模型的分析方法，第一卷
Banasiak, Jacek, Lamb, Wilson, Laurencot, Philippe
- 出版商: CRC
- 出版日期: 2019-09-20
- 售價: $7,140
- 貴賓價: 9.5 折 $6,783
- 語言: 英文
- 頁數: 376
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 149877265X
- ISBN-13: 9781498772655
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商品描述
Analytic Methods for Coagulation-Fragmentation Models is a two-volume set that provides a comprehensive exposition of the mathematical analysis of coagulation-fragmentation models. Initially, an in-depth survey of coagulation-fragmentation processes is presented, together with an account of relevant early results obtained on the associated model equations. These provide motivation for the subsequent detailed treatment of more up-to-date investigations which have led to significant theoretical developments on topics such as solvability and the long-term behaviour of solutions. To make the account as self-contained as possible, the mathematical tools that feature prominently in these modern treatments are introduced at appropriate places. The main theme of Volume I is the analysis of linear fragmentation models, with Volume II devoted to processes that involve the nonlinear contribution of coagulation.
Features of Volume I:
- The main models of the theory together with their derivations and early methods of solution
- A detailed presentation of the operator theoretical methods and semigroup theory that play an essential role in the theory of fragmentation processes
- A comprehensive theory of fragmentation processes, including fragmentation with growth and decay in both the discrete and continuous particle size cases
- An analytical explanation of the pathologies' of the fragmentation equation, such as the shattering phase transition and non-uniqueness of solutions
- An analysis of the long-term dynamics of the discrete size fragmentation equation with growth
商品描述(中文翻譯)
《凝聚-碎裂模型的分析方法》是一本兩卷本的書籍，提供了對凝聚-碎裂模型數學分析的全面闡述。首先，書中深入調查了凝聚-碎裂過程，並介紹了與相關模型方程有關的早期結果。這些結果為隨後對更現代研究的詳細處理提供了動機，這些研究在可解性和解的長期行為等主題上導致了重要的理論發展。為了使內容盡可能自足，書中在適當的地方引入了這些現代處理中突出的數學工具。第一卷的主要主題是線性碎裂模型的分析，而第二卷則專注於涉及凝聚的非線性貢獻的過程。
第一卷的特點：
- 理論的主要模型及其推導和早期解法
- 詳細介紹在碎裂過程理論中起重要作用的算子理論方法和半群理論
- 包括增長和衰減的碎裂過程的全面理論，涵蓋離散和連續粒子大小的情況
- 對碎裂方程的病態現象進行分析，例如破碎相變和解的非唯一性
- 對具有增長的離散大小碎裂方程的長期動力學進行分析
作者簡介
Jacek Banasiak is a Professor of Mathematics at the University of Kwazulu-Natal, Zimbabwe. His main research areas are functional analytic methods in kinetic theory and mathematical biology, singular perturbations, general applied analysis and partial differential equations and evolution problems. He is the author/co-author of 5 monographs and over 100 papers in these fields. He is also Editor-in-Chief of Afrika Matematika (Springer). In 2013 he was awarded the Cross of Merit (Silver) of the Republic of Poland.
Wilson Lamb is a Senior Lecturer at the University of Strathclyde, Scotland. His main interests lie in Functional Analysis, Applied Analysis, Evolution Equations, Mathematical Analysis of Coagulation and Fragmentation Processes. He has published over 45 refereed research publications. He has given lecture courses at all levels to Mathematics degree students and to Science and Engineering students. These include courses on elementary calculus and algebra, discrete mathematics, multivariable calculus, linear algebra and vector space theory. He was nominated for the University of Strathclyde Students' Association Teaching Excellence Awards in 2012, 2013 and 2014; in 2013, he was shortlisted for the category of "Best in Science Faculty."
Philippe Laurençot is the Director of research (senior researcher) CNRS 1, Institut de Math ematiques de Toulouse, Universite Paul Sabatier. His main research interests include the mathematical analysis of evolution partial differential equations, dynamical system approach to evolution partial differential equations, coagulation equations and mathematical models in biology. He is the author of over 170 scientific publications and has given invited talks all over the world.
作者簡介(中文翻譯)
Jacek Banasiak是津巴布韋夸祖魯-納塔爾大學的數學教授。他的主要研究領域包括動力學理論和數學生物學中的函數分析方法、奇異擾動、一般應用分析以及偏微分方程和演化問題。他是這些領域中5本專著和超過100篇論文的作者或合著者。他還是《Afrika Matematika》（Springer）的主編。2013年，他獲得了波蘭共和國的銀獎功勳十字勳章。
Wilson Lamb是蘇格蘭斯特拉斯克萊德大學的高級講師。他的主要興趣在於函數分析、應用分析、演化方程、凝聚和碎裂過程的數學分析。他已發表超過45篇經過同行評審的研究論文。他為數學學位學生以及科學和工程學生提供各級別的講座課程，包括初等微積分和代數、離散數學、多變量微積分、線性代數和向量空間理論。他在2012年、2013年和2014年被提名為斯特拉斯克萊德大學學生會教學卓越獎；在2013年，他入圍了“最佳科學學院”類別。
Philippe Laurençot是法國國家科學研究中心（CNRS 1）圖盧茲數學研究所的研究主任（高級研究員）。他的主要研究興趣包括演化偏微分方程的數學分析、動力系統方法在演化偏微分方程中的應用、凝聚方程以及生物學中的數學模型。他是超過170篇科學出版物的作者，並在全球各地發表過邀請演講。
