  In this paper we introduce a concept of "regulated function" $v(t,x)$ of two
variables, which reduces to the classical definition when $v$ is independent of
$t$. We then consider a scalar conservation law of the form
$u_t+F(v(t,x),u)_x=0$, where $F$ is smooth and $v$ is a regulated function,
possibly discontinuous w.r.t.both $t$ and $x$. By adding a small viscosity, one
obtains a well posed parabolic equation. As the viscous term goes to zero, the
uniqueness of the vanishing viscosity limit is proved, relying on comparison
estimates for solutions to the corresponding Hamilton--Jacobi equation.
  As an application, we obtain the existence and uniqueness of solutions for a
class of $2\times2$ triangular systems of conservation laws with hyperbolic
degeneracy.
