Solution of convection--diffusion equation by the method of characteristics (Q1877226)

The author considers the nonlinear problem: \[ \partial_tu+ F(u) \nabla u-D\Delta u=0;\quad u(0,x)= u_0(x)\;x\in\Omega \] with homogeneous boundary conditions. This problem is solved by the method of characteristics. One of the innovations in the paper is that the velocity field must not be bounded, it is enough to be supposed continuous. The convergence of the method is proved and numerical experiments in one-dimension illustrate the theory.