Optimal control problem and inhomogeneous minimax viscosity solution in L∞ for relativistic Vlasov equation

Abstract

In this work, using an important result of Chen Guiqiang and Su Bo [7], we set a theorem about a global in finite time and local in space existence and uniqueness of a minimax viscosity solution in L¥ of the relativistic Vlasov equation in Yang-Mills charged time oriented four dimensional curved space-time with non-zero mass, therefore derive from it an optimal control problem. To our knowledge, the method used here to derive an existence theorem is original and totally different from the ones used to solve similar problems.