Optimal Control Problems for the Whitham Type Nonlinear Differential Equations with Impulse Effects

In the article the questions of solving optimal control problem for the nonlinear Whitham-type partial differential equations with impulsive effects are studied. The modified method of characteristics allows partial differential equations of the first order to be represented as ordinary differential equations that describe the change of an unknown function along the line of extended characteristics. The unique solvability of the initial value problems for the fixed values of control function is proved by the method of successive approximations and contraction mappings. The quality functional has a quadrate form. The necessary optimality conditions for nonlinear control are formulated. Method of maximum principle is used. The definition of the unknown control function is reduced to solving the nonlinear functional equations.