Nonlinear Functional Analysis with Applications to Combustion Theory
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 prob...
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| Materyal Türü: | Elektronik Ekitap |
| Dil: | İngilizce |
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Springer Nature Switzerland : Imprint: Springer,
2025.
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| Edisyon: | 1st ed. 2025. |
| Seri Bilgileri: | Applied Mathematical Sciences,
221 |
| Konular: | |
| Online Erişim: | https://doi.org/10.1007/978-3-031-85757-7 |
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İçindekiler:
- 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 λ sufficiently small)
- Proof of Theorem 1.10 (Unique solvability for λ 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.