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Using Clifford analysis in a multidimensional space some elliptic, hyperbolic and parabolic systems of partial differential equations are constructed, which are related to the well-known classical equations. To obtain parabolic systems Clifford algebra is modified and some corresponding differential operator is constructed. For systems obtained the boundary and initial value problems are solved.
Integral equations of the form (2) below, dual to (1) are studied from the point of view of finding their effective solutions, the results being given in Section 1. The results are applied in Section 2 for solving nonlocal problems for the polyharmonic functions in the half plane.
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