ENTROPY ESTIMATES FOR CONSERVATION-LAWS

This paper gives some estimates relating to the Oleinik entropy inequa lity for a single conservation law in one space dimension. We define a functional phi(alpha)(T, U, epsilon) and show that it is bounded unif ormly for certain entropy solutions U (and unbounded for rarefaction s hocks) as epsilon --> 0. This suggests that the boundedness of the fun ctionals phi(alpha)(T, U, epsilon) could possibly be viewed as an entr opy condition.