Nonlinearity, conservation law and shocks. 2. Stability consideration and examples

Abstract

In part 1 of this series we explained the concept of genuine nonlinearity, which is responsible for the appearance of discontinuities in a solution which was initially smooth. To include discontinuities in the solution, it became necessary to consider the governing equation in the form of a conservation law. In this part we first discuss an example of a continuous solution satisfying discontinuous initial data. Then we use the stability consideration to fix a unique solution of the conservation law. In the end, we present three examples which show that genuine nonlinearity significantly changes the evolution of the shape of a pulse.