Year: 2010
Journal of Partial Differential Equations, Vol. 23 (2010), Iss. 2 : pp. 158–167
Abstract
In this paper we investigate the equations for light-like extremal surfaces in Minkowski space R^{1+(1+n)}. We show that the light-like assumption is compatible with the Cauchy problem and give a necessary and sufficient condition on the global existence of classical solutions of the Cauchy problem. Based on this, we obtain entire light-like extremal surfaces by solving the Cauchy problem explicitly when such necessary and sufficient condition holds. Finally, some discussions and related remarks are given.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v23.n2.3
Journal of Partial Differential Equations, Vol. 23 (2010), Iss. 2 : pp. 158–167
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Light-like
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Global weak and smooth solutions of the equation for timelike extremal surface in Minkowski space
Lai, Ningan
Liu, Jianli
Journal of Mathematical Analysis and Applications, Vol. 428 (2015), Iss. 2 P.1135
https://doi.org/10.1016/j.jmaa.2015.02.088 [Citations: 3]