商品描述
Explore the fascinating intersection of mathematics and combustion theory in this comprehensive monograph, inspired by the pioneering work of N. N. Semenov and D. A. Frank-Kamenetskii. Delving into the nonlinear functional analytic approach, this book examines semilinear elliptic boundary value problems governed by the Arrhenius equation and Newton's law of heat exchange. Key topics include:
Detailed analysis of boundary conditions, including isothermal (Dirichlet) and adiabatic (Neumann) cases. Critical insights into ignition and extinction phenomena in stable steady temperature profiles, linked to the Frank-Kamenetskii parameter. Sufficient conditions for multiple positive solutions, revealing the S-shaped bifurcation curves of these problems.
Designed for researchers and advanced students, this monograph provides a deep understanding of nonlinear functional analysis and elliptic boundary value problems through their application to combustion and chemical reactor models. Featuring detailed illustrations, clearly labeled figures, and tables, this book ensures clarity and enhances comprehension of complex concepts. Whether you are exploring combustion theory, functional analysis, or applied mathematics, this text offers profound insights and a thorough mathematical foundation.
商品描述(中文翻譯)
探索數學與燃燒理論之間迷人的交集，本綜合專著受到 N. N. Semenov 和 D. A. Frank-Kamenetskii 開創性工作的啟發。深入探討非線性函數分析方法，本書研究由 Arrhenius 方程和牛頓熱交換定律所支配的半線性橢圓邊值問題。
主要主題包括：
- 邊界條件的詳細分析，包括等溫（Dirichlet）和絕熱（Neumann）情況。
- 對穩定穩態溫度分佈中點火和熄滅現象的關鍵見解，與 Frank-Kamenetskii 參數相關聯。
- 多個正解的充分條件，揭示這些問題的 S 形分岔曲線。
本專著旨在為研究人員和高級學生提供對非線性函數分析和橢圓邊值問題的深入理解，通過其在燃燒和化學反應器模型中的應用。書中包含詳細插圖、清晰標示的圖形和表格，確保清晰度並增強對複雜概念的理解。
無論您是在探索燃燒理論、函數分析還是應用數學，本書都提供深刻的見解和全面的數學基礎。
作者簡介
Dr. Kazuaki Taira, born in Tokyo, Japan, on January first 1946, was a professor of mathematics at the University of Tsukuba, Japan (1998-2009). He received his Bachelor of Science degree in 1969 from the University of Tokyo, Japan, and his Master of Science degree in 1972 from Tokyo Institute of Technology, Japan, where he served as an assistant from 1972 to 1978. The Doctor of Science degree was awarded to him on June 21 1976 by the University of Tokyo, and on June 13 1978 the Doctorat d'´Etat (literally 'State Doctorate') degree was given to him by Universit´e de Paris-Sud (Orsay), France. He had been studying there on the French government scholarship from 1976 to 1978. Dr. Taira was also a member of the Institute for Advanced Study (Princeton), U. S. A. (1980-1981), and was an associate professor at the University of Tsukuba (1981-1995), and a professor at Hiroshima University, Japan (1995-1998). In 1998, he accepted the offer from the University of Tsukuba to teach there again as a professor. He was a part-time professor at Waseda University (Tokyo), Japan, from 2009 to 2017. His current research interests are in the study of three interrelated subjects in analysis: semigroups, elliptic boundary value problems and Markov processes.
作者簡介(中文翻譯)
平良和明博士，於1946年1月1日出生於日本東京，曾任日本筑波大學數學教授（1998-2009）。他於1969年獲得東京大學理學學士學位，並於1972年獲得東京工業大學理學碩士學位，並於1972年至1978年擔任該校助理。1976年6月21日，他獲得東京大學的理學博士學位，並於1978年6月13日獲得法國巴黎南方大學（Orsay）的國家博士學位（Doctorat d'État）。他在1976年至1978年間獲得法國政府獎學金在該校學習。平良博士也是美國普林斯頓高等研究院的成員（1980-1981），並曾擔任筑波大學的副教授（1981-1995），以及日本廣島大學的教授（1995-1998）。1998年，他接受筑波大學的邀請，再次擔任教授。他於2009年至2017年間擔任日本早稻田大學的兼任教授。他目前的研究興趣集中在分析中的三個相互關聯的主題：半群、橢圓邊界值問題和馬可夫過程。
