Initial-boundary value problem for the equation of timelike extremal surfaces in Minkowski space

This paper investigate the mixed initial-boundary value problem for the equation of timelike extremal surfaces in Minkowski space R1+(1+n) in the first quadrant. Under the assumptions that the initial data are bounded and the boundary data are small, we prove the global existence and uniqueness of the C-2 solutions of the initial-boundary value problem for this kind of equation. Based on the existence results on global classical solutions, we also show that, as t tends to infinity, the first order derivatives of the solutions approach C-1 traveling wave, under the appropriate conditions on the initial and boundary data. Geometrically, this means the extremal surface approaches a generalized cylinder which is an exact solution. (C) 2008 American Institute of Physics.