The General Theory for Scalar Conservation Laws
摘要
The theory of the scalar balance law, in several spatial dimensions, has reached a state of virtual completeness. In the framework of classical solutions, the elementary, yet effective, method of characteristics yields a sharper version of Theorem 5.1.1, determining explicitly the life span of solutions with Lipschitz continuous initial data and thereby demonstrating that in general this life span is finite. Under generic conditions on the initial data, the breakdown of classical solutions is initiated at a single point in space by wave breaking inducing the development of a shock.