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In this paper, we consider the initial value problem for theEinstein-Vlasov-Scalar field equations in temporal gauge, where the initialdata are prescribed on two characteristic smooth intersecting hypersurfaces.From a suitable choice of some free data, the initial data constraints'sproblem is solved globally, then the evolution problem relative to the deducedinitial data is solved locally in time.

Cauchy problem on two characteristic hypersurfaces for the Einstein-Vlasov-Scalar field equations in temporal gauge