  We use the method of Compensated Compactness and Kinteic Formulation to show
that the almost everywhere limit of quasilinear viscous approximations is the
unique entropy solution (in the sense of {\it F. Otto}) of the corresponding
scalar conservation laws on a bounded domain in $\mathbb{R}^{d}$, where the
viscous term is of the form $\varepsilon\,div\left(B(u^{\varepsilon})\nabla
u^{\varepsilon}\right)$.
