Convergence of approximate solutions to scalar conservation laws by degenerate diffusion (Q915962)

This paper is concerned with the existence of weak solutions to the scalar conservation laws \[ (*)\quad u_ t+f(u)_ x=0,\quad x\in {\mathbb{R}},\quad t>0,\quad u(x,0)=u_ 0(x), \] in the framework provided by compensated compactness. The author shows that the unique weak `entropic' solution to (*) can be obtained by replacing the usual viscous approximation by means of the porous media operator.