Abstract:

Abstract: Nonconvex conservation laws appear naturally as models of the dynamics of materials with phase boundaries, like thin film flows. More generaly, they occur in systems for which the total energy of the molecular system is nonconvex. In such systems, the second law of thermodynamics, which imposes that entropy production be positive, is not sufficient to obtain uniqueness of solutions. In fact, a kinetic relation is necessary to relate the driving force and the speed of the propagating phase boundary. This kinetic relation supplements the usual entropy condition (an inequality) by specifiying the rate of entropy production.

In this talk, we give a general introduction to the theory of convex and nonconvex conservation laws. We conclude with a discussion of more recent results obtained in collaboration with Philippe G. LeFloch of Paris VI.