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

Pages: 381 - 397, Volume 23, Issue 1/2, January/February 2009

doi:10.3934/dcds.2009.23.381       Abstract        Full Text (218.6K)       Related Articles

Jianli Liu - Department of Mathematics, Fudan University, Shanghai, 200433, China (email)
Yi Zhou - Department of Mathematics, Fudan University, Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education of China, Shanghai 200433, China (email)

Abstract: 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.

Keywords:  The equation of time-like extremal surface, initial-boundary value problem, global classical solution
Mathematics Subject Classification:  Primary: 35F99, 35L60; Secondary: 35Q80

Received: August 2007;      Revised: July 2008;      Published: September 2008.