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ABSTRACT In this work, the existence and uniqueness of the solution to the semiperiodic boundary problem for a third‐order partial differential equation are obtained. Estimates for the solution and its derivatives have been established. To achieve this, a special substitution is used to reduce the third‐order equation to a system of ordinary differential equations (ODE) and functional relations. The unique solvability of the resulting periodic boundary value problem for the ODE system is proven using the parameterization method.
Ospanov et al. (Sun,) studied this question.