國立高雄大學圖資館 |

登入

回首頁

Nonlinear functional analysis with applications to combustion theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Nonlinear functional analysis with applications to combustion theoryby Kazuaki Taira.
作者:	Taira, Kazuaki.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xv, 269 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Nonlinear functional analysis.
電子資源:	https://doi.org/10.1007/978-3-031-85757-7
ISBN:	9783031857577$q(electronic bk.)

Nonlinear functional analysis with applications to combustion theory
Taira, Kazuaki.

Nonlinear functional analysis with applications to combustion theory[electronic resource] /by Kazuaki Taira. - Cham :Springer Nature Switzerland :2025. - xv, 269 p. :ill., digital ;24 cm. - Applied mathematical sciences,v. 2212196-968X ;. - Applied mathematical sciences ;v.176..

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.

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.

ISBN: 9783031857577$q(electronic bk.)

Standard No.: 10.1007/978-3-031-85757-7doiSubjects--Topical Terms:

229319
Nonlinear functional analysis.

LC Class. No.: QA321.5

Dewey Class. No.: 515.7

Nonlinear functional analysis with applications to combustion theory
LDR:03535nmm a2200337 a 4500 001 678144
003 DE-He213
005 20250515130316.0
006 m d
007 cr nn 008maaau
008 251021s2025 sz s 0 eng d
020 $a 9783031857577$q(electronic bk.)
020 $a 9783031857560$q(paper)
024 7 $a 10.1007/978-3-031-85757-7 $2 doi
035 $a 978-3-031-85757-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA321.5
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.7 $2 23
090 $a QA321.5 $b .T134 2025
100 1 $a Taira, Kazuaki. $3 357439
245 1 0 $a Nonlinear functional analysis with applications to combustion theory $h [electronic resource] / $c by Kazuaki Taira.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xv, 269 p. : $b ill., digital ; $c 24 cm.
490 1 $a Applied mathematical sciences, $x 2196-968X ; $v v. 221
505 0 $a 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.
520 $a 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.
650 0 $a Nonlinear functional analysis. $3 229319
650 0 $a Combustion $x Mathematical models. $3 234958
650 1 4 $a Functional Analysis. $3 274845
650 2 4 $a Mathematical Physics. $3 522725
650 2 4 $a Mathematical Applications in Chemistry. $3 925513
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Applied mathematical sciences ; $v v.176. $3 557779
856 4 0 $u https://doi.org/10.1007/978-3-031-85757-7
950 $a Mathematics and Statistics (SpringerNature-11649)