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  • 1
    Online Resource
    Online Resource
    Handbook of differential equations; Volume 2 (2005)
    Amsterdam [u.a.] : Elsevier
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    UID:
    b3kat_BV036962353
    Format: 1 Online-Ressource (XI, 663 Seiten)
    ISBN: 0444520481 , 9780444520487
    In: 2
    Language: English
    Subjects: Mathematics
    RVK:
    SK 540
    Keywords: Evolutionsgleichung ; Partielle Differentialgleichung
    URL: Volltext  (URL des Erstveröffentlichers)
    Author information: Feireisl, Eduard 1957-
    Author information: Dafermos, Constantine M. 1941-
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    Online Access
    HWR Berlin
    EUV Frankfurt
    TH Brandenburg
    HTW Berlin
    TH Wildau
    BTU Cottbus
    BHT
  • 2
    Online Resource
    Online Resource
    Evolutionary equations / (2005)
    Boston :Elsevier,
    Details
    UID:
    almafu_9958102863102883
    Format: 1 online resource (677 p.)
    ISBN: 1-280-63849-4 , 9786610638499 , 0-08-046138-7
    Series Statement: Handbook of differential equations ; 2
    Content: The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim
    Note: Description based upon print version of record. , Preface; List of Contributors; Contents; Contents of Volume I; Euler Equations and Related Hyperbolic Conservation Laws; Introduction; Basic features and phenomena; One-dimensional Euler equations; Multidimensional Euler equations and related models; Multidimensional steady supersonic problems; Multidimensional steady transonic problems; Multidimensional unsteady problems; Divergence-measure fields and hyperbolic conservation laws; Acknowledgments; References; Blow-up of Solutions of SupercriticalParabolic Equations; Introduction; Beyond blow-up; Self-similar solutions , Examples of peaking solutions for the Cauchy problemBoundedness of global solutions; Blow-up rate; Convergence to backward self-similar solutions; Connecting equilibria by blow-up solutions; Immediate regularization after blow-up; Multiple blow-up; Grow-up rate; Oscillating grow-up solutions and grow-up set; Acknowledgments; References; The Boltzmann Equation and Its Hydrodynamic Limits; Introduction; Fluid dynamics: A presentation of models; The Boltzmann equation and its formal properties; Hydrodynamic scalings for the Boltzmann equation , Compressible limits of the Boltzmann equation: Formal resultsIncompressible limits of the Boltzmann equation: Formal results; Mathematical theory of the Cauchy problem for hydrodynamic models; Mathematical theory of the Cauchy problem for the Boltzmann equation; The Hilbert expansion method: Application to the compressible Euler limit; The relative entropy method: Application to the incompressible Euler limit; Applications of the moment method; Conclusions and open problems; Acknowledgments; References; Long-Time Behavior of Solutions toHyperbolic Equations with Hysteresis; Introduction , An initial-boundary value problemPeriodic solutions; Hysteresis operators; Acknowledgment; References; Mathematical Issues Concerningthe Navier-Stokes Equations andSome of Its Generalizations; Part A. Incompressible fluids with shear, pressure and density dependent viscosity from the point of view of continuum physics; Introduction; Balance equations; The constitutive models for compressible and incompressible Navier-Stokes fluids and some of their generalizations; Boundary conditions; Part B. Mathematical analysis of flows of fluids with shear, pressure and density dependent viscosity , IntroductionDefinitions of (suitable) weak solutions; Existence of a (suitable) weak solution; On the smoothness of flows; Uniqueness and large-data behavior; On the structure of possible singularities for flows of the Navier-Stokes fluid; Other incompressible fluid models; Acknowledgments; References; Evolution of Rate-Independent Systems; Introduction; The simple case with a quadratic energy; Incremental problems and a priori estimates; Convex energies; Nonconvex and nonsmooth problems; Nonassociated dissipation laws; Applications to continuum mechanics; Acknowledgments; References , On the Global Weak Solutions to a Variational Wave Equation , English
    Additional Edition: ISBN 0-444-52048-1
    Language: English
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    HU Berlin
    FU Berlin
    Charité
  • 3
    Online Resource
    Online Resource
    Handbook of differential equations : Volume 2: Evolutionary equations (2005)
    Amsterdam : Elsevier/North Holland
    Details
    UID:
    gbv_1684904544
    Format: Online-Ressource
    Edition: Reproduktion Elsevier e-book collection on ScienceDirect
    ISBN: 0444520481 , 9780444520487
    Content: The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today. . Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics
    Note: Includes bibliographical references and indexes
    Additional Edition: ISBN 9780444520487
    Additional Edition: ISBN 0444520481
    Additional Edition: ISBN 9780444517449
    Additional Edition: ISBN 0444517448
    Additional Edition: Erscheint auch als Druck-Ausgabe Handbook of differential equations ; Vol. 2 Amsterdam [u.a.] : Elsevier/North Holland, 2005 ISBN 0444520481
    Additional Edition: ISBN 9780444520487
    Additional Edition: Erscheint auch als Druck-Ausgabe
    Language: English
    Keywords: Electronic books ; Handbook ; Electronic books
    URL: Volltext  (Deutschlandweit zugänglich)
    URL: Volltext
    URL: lizenzpflichtig
    URL: Inhaltstext
    Author information: Feireisl, Eduard 1957-
    Author information: Dafermos, Constantine M. 1941-
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    Stabi Berlin
    UB Potsdam
  • 4
    Book
    Book
    Handbook of differential equations : evolutionary equations; 2 (2005)
    Amsterdam [u.a.] : Elsevier
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    UID:
    b3kat_BV020825430
    Format: XI, 663 S.
    Edition: 1. ed.
    ISBN: 0444520481
    In: 2
    Language: English
    Keywords: Evolutionsgleichung ; Partielle Differentialgleichung
    Author information: Dafermos, Constantine M. 1941-
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  • 5
    Online Resource
    Online Resource
    Handbook of differential equations, Volume 2, Evolutionary equations (2006)
    Amsterdam : Elsevier/North Holland
    Details
    UID:
    b3kat_BV039830221
    Format: 1 Online-Ressource (1 online resource)
    Edition: 1st ed
    ISBN: 9780444520487 , 0444520481
    Note: The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today. . Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics , Contents -- Preface -- Euler Equations and Related Hyperbolic Conservations Laws, (G.-Q. Chen) -- Blow-up of Solutions of Supercritical Parabolic Equations, (M. Fila) -- The Boltzmann Equation and Its Hydrodynamic limits, (F. Golse) -- Long-Time Behaviour of Solutions to Hyperbolic Equations with Hysteresis, (P. Krejci) -- Mathematical Issues Concerning the Navier-Stokes Equations and some of their Generalizations, (J. Mlek, K.R. Rajagopal) -- Evolution of Rate-Independent Systems, (A. Mielke) -- On the Global Weak Solutions to a Variational Wave Equation, (P. Zhang, Y. Zheng) , Includes bibliographical references and indexes
    Language: English
    URL: Volltext
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    TH Wildau
  • 6
    Book
    Book
    Handbook of differential equations.; 2 / (2005)
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    Details
    UID:
    almahu_BV025687304
    Format: IX, 663 S.
    Edition: 1. ed
    ISBN: 0-444-52048-1
    Language: English
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    HU Berlin get availability status
  • 7
    Online Resource
    Online Resource
    Handbook of differential equations : evolutionary equations. - Vol. 5 edited by C.M. Dafermos, Milan Pokorny (2004)
    Amsterdam : Elsevier/North Holland
    Details
    UID:
    b3kat_BV039834079
    Format: 1 Online-Ressource (1 online resource)
    Edition: 1st ed
    ISBN: 9780444528483 , 0444528482 , 9780080931975 , 0080931979 , 9780080932590 , 0080932592 , 9780444517449 , 0444517448 , 0444511318 , 9780444511317 , 9780444520487 , 0444520481 , 0444528482 , 9780444528483 , 9780444530349 , 0444530347 , 9780444532220 , 0444532226
    Note: The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's. Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savar discusses the most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionary partial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. , Particular attention is paid to the limits of cell's capability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other. The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function. The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. , The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class of non-linear equations is investigated, with applications to stochastic control and differential games. The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations, parabolic equations with coefficients of low regularity, and some fluid-structure interaction models. - Volume 1 focuses on the abstract theory of evolution - Volume 2 considers more concrete probelms relating to specific applications - Volume 3 reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear PDEs , Includes bibliographical references and indexes , Preface -- Contributors -- 1.L. Ambriosio, G. Savar: Gradient flows of probability measures -- 2.M.A. Herrero: The mathematics of chemotaxis -- 3.N. Masmoudi: Examples of singular limits in hydrodynamics -- 4. C. DeLellis: Notes on hyperbolic systems of conservation laws and transport equations -- 5. G. Rein: Collisionless kinetic equations from astrophysics -- the Vlasov-Poisson system -- 6. H.M. Stochastic representations for non-linear parabolic PDE's -- 7. E. Zuazua Controllability and observability of partial differential equations: Some results and open problems -- Index
    Language: English
    URL: Volltext
    Author information: Feireisl, Eduard 1957-
    Author information: Dafermos, Constantine M. 1941-
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    TH Wildau
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