Kinetic Formulation of Conservation Las [Hardcover]

This book gives a general presentation of the mathematical connections between kinetic theory and conservation laws based on several earlier works with P. L. Lions and E. Tadmor, as well as on more recent developments. The kinetic formalism approach allows the reader to consider Partial Differential Equations, such as some nonlinear conservation laws, as linear kinetic (or semi-kinetic) equations acting on a nonlinear quantity. It also aids the reader with using Fourier transform, regularisation, and moments methods to provide new approaches for proving uniqueness, regularizing effects, and a priori bounds.


1. A brief overview of the kinetic approach
2. The function *y, entropies, and representation of nonlinear functions
3. Kinetic formulation of multidimensional scalar conservation laws
4. Uniqueness of solutions to scalar conservation laws and consequences
5. Cancellation of oscillations, averaging lemmas, regularizing effects
6. Kinetic schemes for SCLs
7. Isentropic gas dynamics
8. Kinetic schemes for gas dynamics
Appendix
Bibliography
Index