Modeling and Computational Methods for Kinetic Equations -

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Résumé :
I. Geometric Operators and the Inde.- Spectral invariants of operators of Dirac type on partitioned manifolds.- Index theory of Dirac operators on manifolds with corners up to codimension two.- Index defects in the theory of spectral boundary value problems.- Cyclic homology and pseudo differential operators, a survey.- Index and secondary index theory for flat bundles with duality.- II. Elliptic Boundary Value Problems.- Toeplitz operators, and ellipticity of boundary value problems with global projection conditions.- On the tangential oblique derivative problem - methods, results, open problems.- A note on boundary value problems on manifolds with cylindrical ends.- Relative elliptic theory.- Appendix. Fourier Integral Operators.- A.1. Homogeneous Lagrangian manifolds.- A.2. Local description of homogeneous Lagrangian manifolds.- A.3. Composition of homogeneous Lagrangian manifolds.- A.4. Definition of Fourier integral operators.- A.5. Pseudodifferential operators as Fourier integral operators.- A.6. Boundedness theorems.- A.7. Composition theorems.- References....

Sommaire:
In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused works. Specific applications presented include plasma kinetic models, traffic flow models, granular media models, and coagulation-fragmentation problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications....

From the reviews: Kinetic models can be used to describe the behaviour of gases and fluids in applications ... . The structure is different from a classical book, as it is actually a collection of scientific papers. ... it is recommended primarily for mathematicians with a high interest in physics, or for theoretical physicists, both of which at least at graduate level, but for those who understand the presented ideas, it might be a highly valuable tool or an inspiration for further research. (Simon Seichter, Simulation News Europe, Vol. 16 (1), 2006)