Katrin Grunert, NTNU – Norwegian University of Science and Technology
Solutions of the Hunter–Saxton equation might enjoy wave breaking in finite time. This means that even classical solutions, in general, do not exist globally, but only locally in time, since their spatial derivative might become unbounded from below pointwise in finite time, while the solution itself remains bounded. Furthermore, energy concentrates on sets of measure zero when wave breaking occurs. Thus the prolongation of solutions beyond wave breaking is non-unique and depends heavily on how the concentrated energy is manipulated. In this talk, we will focus on the influence of the manipulated energy on solutions. In particular, we will show how the choice of the solution is reflected in uniqueness and stability results as well as numerical methods.