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  • 1
    Book
    Book
    Philadelphia, Pa. :Soc. for Industrial and Applied Mathematics,
    UID:
    almafu_BV003657058
    Format: VI, 93 S. : , graph. Darst.
    ISBN: 978-0-89871-225-4
    Series Statement: National Science Foundation / Conference Board of the Mathematical Sciences: CBMS-NSF regional conference series in applied mathematics 53
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Grenzfläche ; Diffusion ; Grenzschicht ; Dynamik ; Diffuse Grenzschicht ; Strömungsmechanik ; Nichtlineare Wellenausbreitung
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  • 2
    Book
    Book
    Berlin ; Heidelberg ; New York :Springer-Verlag,
    UID:
    almafu_BV002256334
    Format: IV, 185 Seiten.
    ISBN: 3-540-09117-3 , 0-387-09117-3
    Series Statement: Lecture notes in biomathematics 28
    Language: English
    Subjects: Biology , Mathematics
    RVK:
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    Keywords: Diffusionsgleichung ; Chemische Reaktion ; Diffusion ; Mathematik
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  • 3
    Book
    Book
    New York [u.a.] :Springer,
    UID:
    almahu_BV004549306
    Format: XIII, 257 S. : Ill., graph. Darst.
    ISBN: 0-387-97583-7 , 3-540-97583-7
    Series Statement: Institute for Mathematics and Its Applications 〈Minneapolis, Minn.〉: The IMA volumes in mathematics and its applications 35
    Language: English
    Subjects: Chemistry/Pharmacy , Physics , Mathematics
    RVK:
    RVK:
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    Keywords: Verbrennung ; Mathematisches Modell ; Verbrennung ; Dynamisches Modell ; Verbrennung ; Aufsatzsammlung ; Konferenzschrift ; Aufsatzsammlung ; Konferenzschrift
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  • 4
    UID:
    almahu_9947363005902882
    Format: XIII, 257 p. , online resource.
    ISBN: 9781461209478
    Series Statement: The IMA Volumes in Mathematics and its Applications, 35
    Content: This IMA Volume in Mathematics and its Applications DYNAMICAL ISSUES IN COMBUSTION THEORY is based on the proceedings of a workshop which was an integral part of the 1989-90 IMA program on "Dynamical Systems and their Applications." The aim of this workshop was to cross-fertilize research groups working in topics of current interest in combustion dynamics and mathematical methods applicable thereto. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, George R. Sell, Paul Fife, Amable Liiian and Foreman Williams for organizing the meeting. We especially thank Paul Fife, Amable Liiilin and Foreman Williams for editing the proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, the National Science Foundation and the Office of Naval Research. Avner Friedman Willard Miller, Jr. ix PREFACE The world ofcombustion phenomena is rich in problems intriguing to the math­ ematical scientist. They offer challenges on several fronts: (1) modeling, which involves the elucidation of the essential features of a given phenomenon through physical insight and knowledge of experimental results, (2) devising appropriate asymptotic and computational methods, and (3) developing sound mathematical theories. Papers in the present volume, which are based on talks given at the Workshop on Dynamical Issues in Combustion Theory in November, 1989, describe how all of these challenges have been met for particular examples within a number of common combustion scenarios: reactiveshocks, low Mach number premixed reactive flow, nonpremixed phenomena, and solid propellants.
    Note: Bifurcation, pattern formation and chaos in combustion -- Mathematical investigation of the cold boundary difficulty in flame propagation theory -- Nonlinear development of low frequency one-dimensional instabilities for reacting shock waves -- Dynamics of laminar triple-flamelet structures in non-premixed turbulent combustion -- Free boundary problems and dynamical geometry associated with flames -- On the dynamics of weakly curved detonations -- Simplified equations for low mach number combustion with strong heat release -- Attractors and turbulence for some combustion models -- Linear stability of one-dimensional detonations -- Discrete modeling of beds of propellant exposed to strong stimulus.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9781461269571
    Language: English
    Keywords: Aufsatzsammlung ; Konferenzschrift
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  • 5
    Online Resource
    Online Resource
    Berlin, Heidelberg :Springer Berlin Heidelberg,
    UID:
    almahu_9947363415702882
    Format: IV, 185 p. , online resource.
    ISBN: 9783642931116
    Series Statement: Lecture Notes in Biomathematics, 28
    Content: Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and of course can interact with real chemical species (ions) which are transported through the membrane. These facts gave rise to Hodgkin's and Huxley's celebrated model for the propagation of nerve signals. On the level of populations, individuals interact and move about, and so it is not surprising that here, again, the simplest continuous space-time interaction-migration models have the same g- eral appearance as those for diffusing and reacting chemical systems.
    Note: Preface and General Introduction -- 1. Modeling Considerations -- 1.1 Basic hypotheses -- 1.2 Redistribution processes -- 1.3 Boundaries and interfaces -- 1.4 Reactions with migration -- 1.5 The reaction mechanism -- 1.6 Positivity of the density -- 1.7 Homogeneous systems -- 1.8 Modeling the rate functions -- 1.9 Colony models -- 1.10 Simplifying the model by means of asymptotics -- 2. Fisher’s Nonlinear Diffusion Equation and Selection-Migration Models -- 2.1 Historical overview -- 2.2 Assumptions for the present model -- 2.3 Reduction to a simpler model -- 2.4 Comments on the comparison of models -- 2.5 The question of formal approximation -- 2.6 The case of a discontinuous carrying capacity -- 2.7 Discussion -- 3. Formulation of Mathematical Problems -- 3.1 The standard problems -- 3.2 Asymptotic states -- 3.3 Existence questions -- 4. The Scalar Case -- 4.1 Comparison methods -- 4.2 Derivative estimates -- 4.3 Stability and instability of stationary solutions -- 4.4 Traveling waves -- 4.5 Global stability of traveling waves -- 4.6 More on Lyapunov methods -- 4.7 Further results in the bistable case -- 4.8 Stationary solutions for x-dependent source function -- 5. Systems: Comparison Techniques -- 5.1 Basic comparison theorems -- 5.2 An example from ecology -- 6. Systems: Linear Stability Techniques -- 6.1 Stability considerations for nonconstant stationary solutions and traveling waves -- 6.2 Pattern stability for a class of model systems -- 7. Systems: Bifurcation Techniques -- 7.1 Small amplitude stationary solutions -- 7.2 Small amplitude wave trains -- 7.3 Bibliographical discussion -- 8. Systems: Singular Perturbation and Scaling Techniques -- 8.1 Fast wave trains -- 8.2 Sharp fronts (review) -- 8.3 Slowly varying waves (review) -- 8.4 Partitioning (review) -- 8.5 Transient asymptotics -- 9. References to Other Topics -- 9.1 Reaction-diffusion systems modeling nerve signal propagation -- 9.2 Miscellaneous -- References.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9783540091172
    Language: English
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  • 6
    Online Resource
    Online Resource
    Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
    UID:
    b3kat_BV039747282
    Format: 1 Online-Ressource (vi, 93 Seiten)
    ISBN: 0898712254 , 9780898712254
    Series Statement: CBMS-NSF regional conference series in applied mathematics 53
    Note: Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader , Includes bibliographical references (s. 83-93) , Internal layers: dynamics of internal layers -- Bistable fronts in an inhomogeneous medium -- Phase field models -- Flame theory: activation energy asymptotics for a one-step reaction -- Stability analysis of simple flames -- Flames due to chain branching -- Complex chemistry -- Electrophoresis: Models and problems -- Isotachophoresis -- Isoelectric focusing -- Waves in excitable and self-oscillatory media: One-dimensional problems -- Inhomogeneous media -- Curvature, corners, and twists -- Rotating waves
    Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 0898712254
    Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 9780898712254
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Nichtlineare Wellenausbreitung ; Grenzschicht ; Dynamik ; Grenzfläche ; Diffusion ; Diffuse Grenzschicht ; Strömungsmechanik
    URL: Volltext  (URL des Erstveröffentlichers)
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  • 7
    UID:
    gbv_228750725
    Format: VII, 259 S.
    ISBN: 0306307510
    Uniform Title: Uravnenija vtorogo porjadka s neotricatelʹnoj charakterističeskoj formoj 〈engl.〉
    Note: Literaturverz. S. 251-259 , Literaturverz. S. 251 - 259
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Elliptische Differentialgleichung ; Ordnung 2
    URL: Cover
    Author information: Olejnik, Olʹga A. 1925-2001
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  • 8
    Book
    Book
    Berlin u.a. :Springer,
    UID:
    kobvindex_ZIB000002292
    Format: 185 S.
    ISBN: 3-540-09117-3
    Series Statement: Lecture notes in biomathematics 28
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  • 9
    Book
    Book
    Philadelphia, PA :SIAM,
    UID:
    kobvindex_ZIB000000623
    Format: 93 S.
    ISBN: 0-89871-225-4
    Series Statement: CBMS-NSF regional conference series in applied mathematics
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  • 10
    Online Resource
    Online Resource
    Philadelphia, Pa. :Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),
    UID:
    almahu_9947357892102882
    Format: 1 electronic text (vi, 93 p.) : , ill., digital file.
    ISBN: 9781611970180 (electronic bk.)
    Series Statement: CBMS-NSF regional conference series in applied mathematics ; 53
    Note: Erratum slip inserted. , Internal layers: dynamics of internal layers -- Bistable fronts in an inhomogeneous medium -- Phase field models -- Flame theory: activation energy asymptotics for a one-step reaction -- Stability analysis of simple flames -- Flames due to chain branching -- Complex chemistry -- Electrophoresis: Models and problems -- Isotachophoresis -- Isoelectric focusing -- Waves in excitable and self-oscillatory media: One-dimensional problems -- Inhomogeneous media -- Curvature, corners, and twists -- Rotating waves. , Also available in print version. , Mode of access: World Wide Web. , System requirements: Adobe Acrobat Reader.
    Additional Edition: Print version: ISBN 0898712254
    Additional Edition: ISBN 9780898712254
    Language: English
    URL: SIAM
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