Shock waves, increase of entropy and loss of information
We discuss, for the simplified model of a single conservation law, the concepts of genuine nonlinearity, breakdown of classical solutions, solutions in the distribution sense and their nonuniqueness, the viscosity method, finite difference methods, and the shock condition. We then discuss, for the scalar model, the compactness of solutions constructed by the viscosity and difference methods, and derive the entropy inequality for such solutions. We derive Glimm's estimate for the total variation of solutions of scalar equations that satisfy the shock condition, and show that a discontinuous solution that satisfies the shock condition also satisfies the entropy condition. Scattered remarks are given about the equations of compressible flow: the increase of entropy, some consequences of Carnot's theorem, and the equipartition of energy in the wake of strong shocks.
- Research Organization:
- New York Univ., NY (USA). Courant Mathematics and Computing Lab.
- DOE Contract Number:
- AC02-76ER03077
- OSTI ID:
- 5648733
- Report Number(s):
- DOE/ER/03077-240; ON: DE85013645
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COMPRESSIBLE FLOW
CONSERVATION LAWS
ENTROPY
FINITE DIFFERENCE METHOD
FLUID FLOW
FLUID MECHANICS
ITERATIVE METHODS
MATHEMATICAL MODELS
MECHANICS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PHYSICAL PROPERTIES
SHOCK WAVES
THERMODYNAMIC PROPERTIES