We prove the convergence of quasilinear parabolic viscous approximations to the entropy solution (in the sense of Bardos-Leroux-Nedelec) of a scalar conservation law, considered on a bounded domain in R d .
Method of compensated compactness is used to show that the almost everywhere limit of quasilinear viscous approximations is the unique entropy solution (in the sense of Bardos et.al [1]) of the corresponding scalar conservation laws in a bounded domain in R d , where the viscous term is of the form εdiv (B(u ε )∇u ε ).
We use velocity averaging lemma to show that the almost everywhere limit of quasilinear viscous approximations is the unique entropy solution (in the sense of F. Otto) of the corresponding scalar conservation laws on a bounded domain in R d , where the viscous term is of the form ε div (B(u ε )∇u ε ) and B ≥ 0.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.