عنوان

Scaling limits and models in physical processes

(Number (ISBN

0817659854

(Number (ISBN

3764359854

(Number (ISBN

9780817659851

(Number (ISBN

9783764359850

Number

b545802

Title Proper

Scaling limits and models in physical processes

General Material Designation

[Book]

First Statement of Responsibility

Carlo Cercignani, David H. Sattinger.

Place of Publication, Distribution, etc.

Basel

Name of Publisher, Distributor, etc.

Birkhäuser Verlag, cop.

Date of Publication, Distribution, etc.

1998

Specific Material Designation and Extent of Item

VI, 190, [1] s. : il. ; 24 cm.

Series Title

DMV Seminar, Bd. 28.

Text of Note

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.

Perturbacja (matematyka)

Class number

Book number

Carlo Cercignani, David H. Sattinger.

Carlo Cercignani

David H Sattinger

Electronic name

[Book]

Y