Mixed boundary value problems with integral conditions for a third-order equation

In this paper, we prove the existence of a unique solution to non-local problems in a rectangular domain for a third-order partial differential equation with the thermal conductivity operator in the main part. Methods of the theory of differential equations, the Green's function and the theory of integral equations are used to prove the solvability of the problem. The problems under study are reduced to the equivalent Volterra integral equation of the second kind, which is certainly solvable .

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