Kinetic Formulation of Conservation LawsClarendon Press, 05.12.2002 - 198 Seiten 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. 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. 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. |
Inhalt
1 | 1 |
1 | 12 |
6 | 21 |
8 | 28 |
Notation and preliminaries | 57 |
4 | 85 |
Cancellation of oscillations averaging lemmas regularizing effects | 113 |
60 | 123 |
6 | 125 |
7 | 140 |
The special case y 3 | 156 |
Kinetic schemes for gas dynamics | 167 |
Appendix | 179 |
65 | 187 |
| 197 | |
Häufige Begriffe und Wortgruppen
assumptions averaging lemmas Bo(t Boltzmann equation C(R+ choice compactness concludes the proof consider convergence rate convex entropies convex function deduce defined density derived Dirac masses discrete flux distributional sense dt dx dx d entropy inequalities entropy solution equilibrium Euler equations family of entropies finite volume method initial data values integration isentropic gas dynamics kinetic equation kinetic formulation kinetic representation Kinetic schemes kinetic solution L¹(R L¹(Rd L¹(Rd+1 Lipschitz continuous LP norms Math modulus of continuity nonlinear nonnegative notation notice obtain Perthame Proof of Lemma Proof of Theorem Proposition prove qu² Rd Rd Rd+1 RdxR regularizing effect regularizing kernel result right-hand side satisfies scalar conservation laws Section system of isentropic uniqueness vanishes variables weak entropies weak limits Young measure αξ ди дх
Verweise auf dieses Buch
Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation ... François Bouchut Eingeschränkte Leseprobe - 2004 |
Analytical Approaches to Multidimensional Balance Laws Olga S. Rozanova Eingeschränkte Leseprobe - 2006 |