Hyperbolic conservation law

Summary

A hyperbolic conservation law is a system of conservation laws whose flux Jacobian, in every direction, has real eigenvalues and a full set of eigenvectors. The eigenvalues are the speeds at which small disturbances travel, so information moves at finite speed along several families of waves. The equations of gas dynamics, shallow water and traffic flow are of this type. Their solutions typically form shock waves, and the main results concern weak entropy solutions. See the definition.