I will consider the scalar conservation laws in one space dimension with convex flus. For example, non viscous Burger's equation is one of the examples.   

In this talk, I will explain how the solution behaves for all time and deduce  

(i) Estimate the number of shocks as time goes to infinity,  

(ii) Solution to the problem of controllability and optimal controllability,  

(iii) regularity of entropy solutions.