Inverse Problems with Integral Overdetermination Conditions for the Generalized Korteweg–de Vries (KdV) Equation on a bounded Interval

This talk examines three inverse problems for the generalized Korteweg–de Vries equation on a bounded interval. The main result is a proof of the existence, uniqueness, and Lipschitz continuity of solutions. Depending on the problem, either the unknown right-hand side of the equation,or the boundary condition, or both are recovered simultaneously based on one or two integral conditions on the solution. A key difference from previous studies is the absence of any restrictions on the rate of nonlinearity growth. This was made possible by choosing time-regular function classes. Correctness is established under the condition of small input data or a small time interval.