Unique Solvability of an Initial–Boundary Value Problem for a System of Third-Order Partial Differential Equations

Assanova A.T.
January 2021 Pleiades journals

Differential Equations
2021 #57 Issue 1 111 - 116 pp.

Abstract: We consider an initial–boundary value problem for a system of third-order partialdifferential equations in a rectangular domain. By introducing a new unknown function, we reducethe problem to an equivalent one consisting of a nonlocal problem for a system of second-orderhyperbolic equations with parameters and integral relations. An iterative algorithm is proposedfor approximately solving the equivalent problem, and its convergence is proved. Sufficientconditions in terms of the input data are established for the existence of a unique classical solutionof the original problem.

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Institute of Mathematics and Mathematical Modeling, Ministry of Education andScience, Almaty, 05010, Kazakhstan

Institute of Mathematics and Mathematical Modeling

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