Georgia Institute of Technology College of Sciences

This talk considers a scalar conservation (balance) law equation with random (martingale measure) source term. A new notion of entropic solution is introduced as the underlying calculus for change of variable needs to be changed into Ito's calculus. This is due to irregularities in the trajectory of particles caused by randomness. In the new notion, entropy production has additional terms. We discuss ways to handle such term so that a uniqueness theory can still be established. Additionally, stochastic generalizations of compensated compactness will be given. This was a joint work with David Nualart. It appeared in Journal of Functional Analysis, Vol 255, Issue 2, 2008, pages 313-373.