De-Xing Kong
Jiao Tong University, Shanghai
In this talk, we introduce the appropriate definitions of "linear degeneracy" and "genuine nonlinearity" for quasilinear hyperbolic systems in several space variables, which coincide with the usual ones in one space dimension, and give some applications. In particular, we investigate the equations for $n$-dimensional time-like extremal submanifolds in the Minkowski space, which can be used to describe the dynamics of relativistic strings and membranes moving in the Minkowski space, and present some results on the global existence of smooth solutions for such a kind of equations.