Hyperbolic Conservation Laws
- Conservation law
Several physical laws state that certain basic quantities such as mass, energy, or electric charge are globally conserved. A conservation law is a mathematical equation describing how the density of a conserved quantity varies in time. It is formulated as a partial differential equation having divergence form.
- Flux function
The flux of a conserved quantity is a vector field describing how much of the given quantity moves across any surface at a given time.
Solutions to conservation laws often develop shocks, i.e., surfaces across which the basic physical fields are discontinuous. Knowing the two limiting values of a field on opposite sides of a shock, one can determine the speed of propagation of a shock in terms of the Rankine–Hugoniot equations.
Entropy is an additional quantity which is globally conserved for every smooth solution to a system of conservation laws. In general, however, entropies are not conserved by solutions containing shocks....
KeywordsWeak Solution Space Dimension Hyperbolic System Riemann Problem Piecewise Constant Function
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