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We present a method for solving a class of optimal control problems involving hyperbolic partial differential equations. A numerical integration method for the solution of a general linear second-order hyperbolic partial differential equation representing the type of dynamics under consideration is given. The method, based on the piecewise bilinear finite element approximation on a rectangular mesh, is explicit. The optimal control problem is thus discretized and reduced to an ordinarydoi:10.1017/s0334270000012510 fatcat:n6lpvjo5ojhpbe4cc3mlremy4u