The equation for time-like extremal surfaces in Minkowski space R2+n -: art. no. 013503

In this paper we investigate the equation for time-like extremal surfaces in the Minkowski space R2+n, and show that this kind of equation enjoys many interesting properties nonstrict hyperbolicity, constant multiplicity of eigenvalues, boundedness of characteristic propagation speeds, linear degeneracy of all characteristic fields, richness, etc. Without any smallness assumption of initial data, we give the necessary and sufficient condition on the global existence of classical solutions of the Cauchy problem. Based on this, we prove some global existence theorems on classical solutions of the Dirichlet problem and Neumann problem for this kind of equation. Finally, we present an explicit exact representation, involving two independent arbitrary functions of general solution. (c) 2006 American Institute of Physics.