Control Problems with an Integral Condition for Korteweg–de Vries Equation on Unbounded Domains

The initial and initial-boundary value problems, posed on infinite domains for Korteweg–de Vries equation, are considered. The right-hand side of the equation contains an unknown function, regarded as a control, which must be chosen such that the corresponding solution should satisfy certain additional integral condition. Results on existence and uniqueness are established in the cases of small input data or small time interval.