Explicit construction of measure solutions of Cauchy problem for transportation equations

The transportation equations are a mathematical model of zero-pressure flow in gas dynamics and the adhesion particle dynamics system to explain the formation of large scale structures in the universe.With the help of convex hull of a potential function,the solution is explicitly constructed here.It is straightforward to prove that the solution is a global measure one.And Dirac delta-shocks explained as the concentration of particles may develop in the solution.