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.

  Autorentext

  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.