ON DIRECT AND INVERSE PROBLEMS FOR SYSTEMS OF ODD-ORDER QUASILINEAR EVOLUTION EQUATIONS

Direct and inverse initial-boundary problems on a bounded interval for systems of odd-order quasilinear evolution equations with general nonlinearities are considered. In the case of inverse problems conditions of integral overdetermination are introduced and right-hand sides of equations of special types are chosen as controls. Results on well-posedness of such problems are established. Assumptions on smallness of the input data or smallness of a time interval are required. © (2024), (L.N. Gumilyov Eurasian National University). All rights reserved.