Abstract
The problems of the unique classical solvability and the construction of a solution of a multidimensional mixed problem for a homogeneous fourth order partial integro-differential equations with a degenerate kernel are studied. The multidimensional Fourier series method, based on the separation of many variables, is used. A system of countable systems of algebraic equations is derived. Iteration process of solving the problem is constructed. Sufficient coefficient conditions for the unique classical solvability of the mixed problem are established.
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