For the first time, an exact solution of the three-dimensional Wiener-Hopf integral equation is given, one-dimensional and two-dimensional versions of which are widely used in mixed, including contact problems. The equation in question can be abstractly represented as the action of a three-dimensional stamp on a four-dimensional half-space or layer. In the work, in relation to contact problems of mechanics, as well as seismology, an application of this method was found. It consists in the fact that along with two geometric coordinates, the time coordinate extending along the entire axis is taken as the third. It allows you to introduce a change of condition at zero for stresses, moving in the contact zone from their values to their velocities. Attempts at an analytical or numerical solution of this problem are not known to the authors. The results may be useful in the fields of using the Wiener-Hopf equation in probability theory and statistics, where one-dimensional variants are used, as well as in seismology. Just as in the two-dimensional case, a universal modeling method based on block elements is used in the study.
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