Scalar conservation laws with discontinuous fluxes in one space dimension

In this talk we consider the following conservation law: 

u_t + F(x,t)_x = 0 x in R and t > 0,

u(x,0) = u_0(x).

If F is smooth in both the variables, this problem has been studied extensively and obtained the existence and uniqueness of entropy solutions by Lax, Olenik and Kruzkov. However if the flux F is not smooth in x variable,say having finite number of discontinuities,(such situations arises in two phase flow problems) then the problem of finding the proper interphase entropy condition so that the problem admits a unique solution. Here I would discuss the entropy theries, existence, uniqueness of solutions and convergence of numerical schemes.