January & February  2009, 23(1&2): 381-397. doi: 10.3934/dcds.2009.23.381

The initial-boundary value problem on a strip for the equation of time-like extremal surfaces

1. 

Department of Mathematics, Fudan University, Shanghai, 200433, China

2. 

Department of Mathematics, Fudan University, Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education of China, Shanghai 200433

Received  August 2007 Revised  July 2008 Published  September 2008

In this paper we study the mixed initial-boundary value problem for the equation of time-like extremal surfaces in Minkowski space $R^{1+(1+n)}$ on the strip $R^{+}\times[0,1]$. Under the assumptions that the boundary data are small and decaying, we get the global existence and uniqueness of classical solutions.
Citation: Yi Zhou, Jianli Liu. The initial-boundary value problem on a strip for the equation of time-like extremal surfaces. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 381-397. doi: 10.3934/dcds.2009.23.381
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