Inverse problems with integral conditions for the generalized Korteweg-de Vries equation

Results on well-posedness of three inverse problems with integral conditions on a bounded interval for the generalized Korteweg-de Vries equation without any restrictions on the growth rate of nonlinearity are established. Either the right-hand side of equation or the boundary data, or both are chosen as controls. The considered solutions are regular with respect to the time variable. Assumptions on smallness of the input data or smallness of a time interval are required.