The existence, uniqueness and continuous dependence of global weak solutions of coupled sine-Gordon equations are established in the framework of variational method due to Dautray and Lions. As an application of weak solutions, we solve the quadratic optimal control problems for the control systems described by coupled sine-Gordon equations.
"COUPLED SINE-GORDON EQUATIONS AS NONLINEAR SECOND ORDER EVOLUTION EQUATIONS." Taiwanese J. Math. 5 (2) 297 - 315, 2001. https://doi.org/10.11650/twjm/1500407338