For odd-order quasilinear evolution systems on a bounded interval, unique weak solutions exist under smallness assumptions, and inverse problems with several integral overdetermination conditions have unique controls.
Faminskii, Controllability problems for the Korteweg–de Vries equati on with integral overdetermination
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On direct and inverse problems for odd-order systems of quasilinear evolution equations
For odd-order quasilinear evolution systems on a bounded interval, unique weak solutions exist under smallness assumptions, and inverse problems with several integral overdetermination conditions have unique controls.