Nonlinear Functional Analysis with Applications to Combustion Theory: 221

“The appendix presents maximum principles for second-order, uniformly elliptic differential operators with real coefficients. The structure of the book is very clear, the proof of each result is given with details, the author illustrating key points with appropriate figures and the structure of the proofs with flowcharts pointing to the tools presented in the intermediate chapters. Each chapter ends with notes and comments.” (Alain Brillard, zbMATH 1568.80001, 2025)

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.