Kinetic Formulation of Conservation Laws
«The book is a good introduction into the theory of kinetic formulations of conservation laws written by the leading expert in the field. A list of open problems and the extensive bibliography also makes it a starting point for further research.»
Zentralblatt MATH
This book gives a general presentation of the mathematical and numerical connections kinetic theory and conservation laws based on several earlier works with P. L. Lions and E. Tadmor, as well as on more recent developments. Les mer
using Fourier transform, regularisation, and moments methods to provide new approaches for proving uniqueness, regularizing effects, and a priori bounds.
Special care has been given to introduce basic tools, including the classical Boltzmann formalism to derive compressible fluid dynamics, the study of oscillatons through the kinetic defect measure, and an elementary construction of solutions to scalar conservation laws. More advanced material contains regularizing effects through averaging lemmas, existence of global large solutions to isentropic gas dynamics, and a new uniqueness proof for scalar conservation laws. Sections are also devoted to
the derivation of numerical approaches, the 'kinetic schemes', and the analysis of their theoretical properties.
Detaljer
- Forlag
- Oxford University Press
- Innbinding
- Innbundet
- Språk
- Engelsk
- ISBN
- 9780198509134
- Utgivelsesår
- 2002
- Format
- 24 x 16 cm
Anmeldelser
«The book is a good introduction into the theory of kinetic formulations of conservation laws written by the leading expert in the field. A list of open problems and the extensive bibliography also makes it a starting point for further research.»
Zentralblatt MATH