Kazuaki Taira

Nonlinear Functional Analysis with Applications to Combustion Theory

• Gebundenes Buch

Produktbeschreibung

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 reactormodels. 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.

Produktdetails

• Applied Mathematical Sciences 221
• Verlag: Springer / Springer Nature Switzerland / Springer, Berlin
• Artikelnr. des Verlages: 978-3-031-85756-0
• Seitenzahl: 288
• Erscheinungstermin: 15. Mai 2025
• Englisch
• Abmessung: 241mm x 160mm x 22mm
• Gewicht: 543g
• ISBN-13: 9783031857560
• ISBN-10: 3031857569
• Artikelnr.: 73009896

Autorenporträt

Dr. Kazuaki Taira was awarded a Doctor of Science degree by the University of Tokyo (1976) and a Doctorat d'État degree by Université de Paris-Sud (Orsay) (1978), where he had studied on a French government scholarship (1976-1978). He was also a member of the Institute for Advanced Study (Princeton) (1980-1981), an associate professor at the University of Tsukuba (1981-1995), and a professor at Hiroshima University (1995-1998). In 1998, he accepted an offer from the University of Tsukuba to teach there again as a professor. He was also a part-time professor at Waseda University (2009-2017). His current research interests are in three interrelated subjects in analysis: semigroups, elliptic boundary value problems and Markov processes.

Inhaltsangabe

Preface.- Introduction and Main Results.- Part I. A Short Course in Nonlinear Functional Analysis.- Elements of Degree Theory.- Theory of Positive Mappings in Ordered Banach Spaces.- Elements of Bifurcation Theory.- Part II. Introduction to Semilinear Elliptic Problems via Semenov Approximation.- Elements of Functions Spaces.- Semilinear Hypoelliptic Robin Problems via Semenov Approximation.- Spectral Analysis of the Closed Realization A.- Local Bifurcation Theorem for Problem (6.4).- Fixed Point Theorems in Ordered Banach Spaces.- The Super-subsolution Method.- Sublinear Hypoelliptic Robin Problems.- Part III. A Combustion Problem with General Arrhenius Equations and Newtonian Cooling.- Proof of Theorem 1.5 (Existence and Uniqueness).- Proof of Theorem 1.7 (Multiplicity).- Proof of Theorem 1.9 (Unique solvability for sufficiently small).- Proof of Theorem 1.10 (Unique solvability for sufficiently large).- Proof of Theorem 1.11 (Asymptotics).- Part IV. Summary and Discussion.- Open Problems in Numerical Analysis.- Concluding Remarks.- Part V Appendix.- A The Maximum Principle for Second Order Elliptic Operators.- Bibliography.- Index.