Unique Solvability of an Initial–Boundary Value Problem for aSystem of Third-Order PartialDifferential Equations

We consider an initial–boundary value problem for a system of third-order partial differential equations in a rectangular domain. By introducing a new unknown function, we reduce the problem to an equivalent one consisting of a nonlocal problem for a system of second-order hyperbolic equations with parameters and integral relations. An iterative algorithm is proposed for approximately solving the equivalent problem, and its convergence is proved. Sufficient conditions in terms of the input data are established for the existence of a unique classical solution of the original problem.

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