Holdings: Scaling limits and models in physical processes

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Bibliographic Details
Title:	Scaling limits and models in physical processes
From:	Carlo Cercignani ; David H. Sattinger
Person:	Cercignani, Carlo 1939-2010 Verfasser aut Sattinger, David H.
Main Authors:	Cercignani, Carlo 1939-2010 (Author), Sattinger, David H. (Author)
Format:	Book
Language:	German
Published:	Basel ; Boston ; Berlin Birkhäuser 1998
Series:	Deutsche Mathematiker-Vereinigung: DMV-Seminar 28
Notation:	SK 540 SK 950 UX 1200
Subjects:	Integrables System Kinetische Gastheorie Skalierungsgesetz Nichtlineare partielle Differentialgleichung
Online Access:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008200008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	VI, 190 S. graph. Darst.
ISBN:	3764359854 0817659854

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MARC


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Record in the Search Index

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adam_text	Contents I Scaling and Mathematical Models in Kinetic Theory Preface 3 1 Boltzmann Equation and Gas Surface Interaction 1.1 Introduction 5 1.2 The Boltzmann equation 6 1.3 Molecules different from hard spheres 11 1.4 Collision invariants 13 1.5 The Boltzmann inequality and the Maxwell distributions 16 1.6 The macroscopic balance equations 17 1.7 The H theorem 22 1.8 Equilibrium states and Maxwellian distributions 24 1.9 Model equations 25 1.10 Boundary conditions 28 Bibliography 34 2 Perturbation Methods for the Boltzmann Equation 2.1 Introduction 37 2.2 Rarefaction regimes 39 2.3 Solving the Boltzmann equation. Analytical techniques 40 2.4 Hydrodynamical limit and other scalings 44 2.5 The linearized collision operator 46 2.6 The basic properties of the linearized collision operat or 48 2.7 Spectral properties of the Fourier transformed, linearized Boltzmann equation 54 2.8 The asymptotic behavior of the solution of the Cauchy problem for the linearized Boltzmann equation 58 2.9 A quick survey of the global existence theorems for the nonlinear equation 60 2.10 Hydrodynamical limits. A formal discussion 63 2.11 The Hilbert expansion 66 2.12 The entropy approach to the hydrodynamical limit 68 2.13 The hydrodynamic limit for short times 72 2.14 Other scalings and the incompressible Navier Stokes equations . . 74 2.15 Concluding remarks 78 Bibliography 80 Index 83 vi Contents II Scaling, Mathematical Modelling, Integrable Systems Preface 89 1 Dispersion 1.1 Introduction 91 1.2 Group and phase velocities 92 2 Nonlinear Schrodinger Equation 2.1 Multiple scales expansion 101 2.2 Pulse solutions 104 3 Korteweg de Vries 3.1 Background and history 107 3.2 Plasmas 111 3.3 Water waves 114 3.4 The solitary wave of the KdV equation 120 4 Isospeetral Deformations 4.1 The KdV hierarchy 123 4.2 The AKNS hierarchy 127 5 Inverse Scattering Theory 5.1 The Schrodinger equation 131 5.2 First Order Systems 142 5.3 Decay of the scattering data 150 6 Variational Methods 6.1 Water Waves 153 6.2 Method of Averaging 155 7 Weak and Strong Nonlinearities 7.1 Breaking and Peaking 161 7.2 Strongly nonlinear models 164 7.3 The extended AKNS hierarchy 170 8 Numerical Methods 8.1 The finite Fourier transform 175 8.2 Pseudospectral codes 182 Bibliography 186 Index 191
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author	Cercignani, Carlo 1939-2010 Sattinger, David H.
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indexdate	2024-12-20T10:24:30Z
institution	BVB
isbn	3764359854 0817659854
language	German
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-008200008
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series	Deutsche Mathematiker-Vereinigung: DMV-Seminar
series2	Deutsche Mathematiker-Vereinigung: DMV-Seminar
spellingShingle	Cercignani, Carlo 1939-2010 Sattinger, David H. Scaling limits and models in physical processes Deutsche Mathematiker-Vereinigung: DMV-Seminar Integrables System (DE-588)4114032-1 gnd Kinetische Gastheorie (DE-588)4163881-5 gnd Skalierungsgesetz (DE-588)4205012-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd
subject_GND	(DE-588)4114032-1 (DE-588)4163881-5 (DE-588)4205012-1 (DE-588)4128900-6
title	Scaling limits and models in physical processes
title_auth	Scaling limits and models in physical processes
title_exact_search	Scaling limits and models in physical processes
title_full	Scaling limits and models in physical processes Carlo Cercignani ; David H. Sattinger
title_fullStr	Scaling limits and models in physical processes Carlo Cercignani ; David H. Sattinger
title_full_unstemmed	Scaling limits and models in physical processes Carlo Cercignani ; David H. Sattinger
title_short	Scaling limits and models in physical processes
title_sort	scaling limits and models in physical processes
topic	Integrables System (DE-588)4114032-1 gnd Kinetische Gastheorie (DE-588)4163881-5 gnd Skalierungsgesetz (DE-588)4205012-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd
topic_facet	Integrables System Kinetische Gastheorie Skalierungsgesetz Nichtlineare partielle Differentialgleichung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008200008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000020322
work_keys_str_mv	AT cercignanicarlo scalinglimitsandmodelsinphysicalprocesses AT sattingerdavidh scalinglimitsandmodelsinphysicalprocesses

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