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" Scaling limits and models in physical processes "
Carlo Cercignani, David H. Sattinger.
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BL
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| Record Number
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726070
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b545802
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| Main Entry
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Carlo Cercignani, David H. Sattinger.
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| Title & Author
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Scaling limits and models in physical processes\ Carlo Cercignani, David H. Sattinger.
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| Publication Statement
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Basel: Birkhäuser Verlag, cop., 1998
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| Series Statement
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DMV Seminar, Bd. 28.
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VI, 190, [1] s. : il. ; 24 cm.
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| ISBN
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0817659854
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: 3764359854
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: 9780817659851
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: 9783764359850
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| Contents
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I Scaling and Mathematical Models in Kinetic Theory.- 1 Boltzmann Equation and Gas Surface Interaction.- 1.1 Introduction.- 1.2 The Boltzmann equation.- 1.3 Molecules different from hard spheres.- 1.4 Collision invariants.- 1.5 The Boltzmann inequality and the Maxwell distributions.- 1.6 The macroscopic balance equations.- 1.7 The H-theorem.- 1.8 Equilibrium states and Maxwellian distributions.- 1.9 Model equations.- 1.10 Boundary conditions.- 2 Perturbation Methods for the Boltzmann Equation.- 2.1 Introduction.- 2.2 Rarefaction regimes.- 2.3 Solving the Boltzmann equation. Analytical techniques.- 2.4 Hydrodynamical limit and other scalings.- 2.5 The linearized collision operator.- 2.6 The basic properties of the linearized collision operator.- 2.7 Spectral properties of the Fourier-transformed, linearized Boltzmann equation.- 2.8 The asymptotic behavior of the solution of the Cauchy problem for the linearized Boltzmann equation.- 2.9 A quick survey of the global existence theorems for the nonlinear equation.- 2.10 Hydrodynamical limits. A formal discussion.- 2.11 The Hilbert expansion.- 2.12 The entropy approach to the hydrodynamical limit.- 2.13 The hydrodynamic limit for short times.- 2.14 Other scalings and the incompressible Navier-Stokes equations.- 2.15 Concluding remarks.- II Scaling, Mathematical Modelling, & Integrable Systems.- 1 Dispersion.- 1.1 Introduction.- 1.2 Group and phase velocities.- 2 Nonlinear Schroedinger Equation.- 2.1 Multiple scales expansion.- 2.2 Pulse solutions.- 3 Korteweg-de Vries.- 3.1 Background and history.- 3.2 Plasmas.- 3.3 Water waves.- 3.4 The solitary wave of the KdV equation.- 4 Isospectral Deformations.- 4.1 The KdV hierarchy.- 4.2 The AKNS hierarchy.- 5 Inverse Scattering Theory.- 5.1 The Schroedinger equation.- 5.2 First Order Systems.- 5.3 Decay of the scattering data.- 6 Variational Methods.- 6.1 Water Waves.- 6.2 Method of Averaging.- 7 Weak and Strong Nonlinearities.- 7.1 Breaking and Peaking.- 7.2 Strongly nonlinear models.- 7.3 The extended AKNS hierarchy.- 8 Numerical Methods.- 8.1 The finite Fourier transform.- 8.2 Pseudospectral codes.
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| Subject
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Perturbacja (matematyka)
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| LC Classification
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QC174.85.S34C375 1998
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Carlo Cercignani
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David H Sattinger
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