Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 163, pp. 1-22.

Title: Goursat problem for the Yang-Mills-Vlasov system
       in temporal gauge

Authors: Marcel Dossa (Univ. de Yaounde I, Cameroun)
         Marcel Nanga (Univ. de N'Djamena, Tchad)
	
Abstract:
 This article studies the characteristic Cauchy
 problem for the Yang-Mills-Vlasov (YMV) system in temporal gauge,
 where the initial data are specified on two intersecting
 smooth characteristic hypersurfaces of Minkowski spacetime
 $(\mathbb{R}^{4},\eta )$.
 Under a $\mathcal{C}^{\infty }$ hypothesis on the data,
 we solve the initial constraint problem and the evolution problem.
 Local in time existence and uniqueness results are established
 thanks to a suitable combination of the method of characteristics,
 Leray's Theory of hyperbolic systems and techniques
 developed by  Choquet-Bruhat for ordinary spatial Cauchy
 problems related to (YMV) systems.

Submitted July 16, 2010. Published December 13, 2011.
Math Subject Classifications: 81Q13, 35L45,35L55.
Key Words: Goursat problem; characteristic initial hypersurfaces; 
           Yang-Mills-Vlasov system; temporal gauge; initial
           constraints; evolution problem.