A kinetic equation with kinetic entropy functions for scalar conservation laws. Final report

Technical Report · Mon Jan 01 04:00:00 EST 1990

OSTI ID:7132767

Perthame, B; Tadmor, E

A nonlinear kinetic equation is constructed and proved to be well-adapted to describe general multidimensional scalar conservation laws. In particular, it is proved to be well-posed uniformly in epsilon - the microscopic scale. It is also shown that the proposed kinetic equation is equipped with a family of kinetic entropy functions - analogous to Boltzmann's microscopic H-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, it is proved by both - BV compactness arguments in the one-dimensional case, that the local density of kinetic particles admits a continuum limit, as it converges strongly with epsilon below 0 to the unique entropy solution of the corresponding conservation law.

• Research Organization: National Aeronautics and Space Administration, Hampton, VA (USA). Inst. for Computer Applications in Science and Engineering
• OSTI ID: 7132767
• Report Number(s): N-90-17401; NASA-CR--181985; NAS--1.26:181985; ICASE--90-11
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
DATA
DOCUMENT TYPES
ENTROPY
EQUATIONS
INFORMATION
KINETIC EQUATIONS
NUMERICAL DATA
PHYSICAL PROPERTIES
PROGRESS REPORT
SCALARS
THEORETICAL DATA
THERMODYNAMIC PROPERTIES
VOID FRACTION