LEADER 04698nam 22006855 450 001 9911003689203321 005 20260209114632.0 010 $a9783031857577 024 7 $a10.1007/978-3-031-85757-7 035 $a(CKB)38815758900041 035 $a(DE-He213)978-3-031-85757-7 035 $a(MiAaPQ)EBC32112449 035 $a(Au-PeEL)EBL32112449 035 $a(OCoLC)1524423203 035 $a(EXLCZ)9938815758900041 100 $a20250515d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNonlinear Functional Analysis with Applications to Combustion Theory /$fby Kazuaki Taira 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (XV, 269 p. 65 illus.) 225 1 $aApplied Mathematical Sciences,$x2196-968X ;$v221 311 08$a9783031857560 327 $aPreface -- 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. 330 $aExplore the fascinating intersection of mathematics and combustion theory in this comprehensive monograph, inspired by the pioneering work of N. N. Semenov and D. A. Frank-Kamenetskii. Delving into the nonlinear functional analytic approach, this book examines semilinear elliptic boundary value problems governed by the Arrhenius equation and Newton's law of heat exchange. Key topics include: Detailed analysis of boundary conditions, including isothermal (Dirichlet) and adiabatic (Neumann) cases. Critical insights into ignition and extinction phenomena in stable steady temperature profiles, linked to the Frank-Kamenetskii parameter. Sufficient conditions for multiple positive solutions, revealing the S-shaped bifurcation curves of these problems. Designed for researchers and advanced students, this monograph provides a deep understanding of nonlinear functional analysis and elliptic boundary value problems through their application to combustion and chemical reactor models. Featuring detailed illustrations, clearly labeled figures, and tables, this book ensures clarity and enhances comprehension of complex concepts. Whether you are exploring combustion theory, functional analysis, or applied mathematics, this text offers profound insights and a thorough mathematical foundation. 410 0$aApplied Mathematical Sciences,$x2196-968X ;$v221 606 $aFunctional analysis 606 $aMathematical physics 606 $aChemometrics 606 $aFunctional Analysis 606 $aMathematical Physics 606 $aMathematical Applications in Chemistry 606 $aCombustió$2thub 606 $aAnàlisi funcional$2thub 606 $aAnàlisi funcional no lineal$2thub 606 $aEstadística matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aFunctional analysis. 615 0$aMathematical physics. 615 0$aChemometrics. 615 14$aFunctional Analysis. 615 24$aMathematical Physics. 615 24$aMathematical Applications in Chemistry. 615 7$aCombustió 615 7$aAnàlisi funcional 615 7$aAnàlisi funcional no lineal 615 7$aEstadística matemàtica 676 $a515.7 700 $aTaira$b Kazuaki$4aut$4http://id.loc.gov/vocabulary/relators/aut$059537 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911003689203321 996 $aNonlinear Functional Analysis with Applications to Combustion Theory$94385264 997 $aUNINA