Study of hyperbolic systems

In this report, we define the conservation form of PDF with initial data .We noticed that even though the initial data is smooth after finite time the solution will be collapsed, means we will not get smooth solution. We defined the weak solution for Conservation laws and then derived Rankine Hugoniot jump conditions. To obtain unique solution of Conservation law, we defined two types of entropy conditions. Finally, we discussed Riemann problem for Scalar Conservation law as well as systems and then discussed the solution for them