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Abstract
In this paper, a new approach for solving partial differential equations by means of multiple Laplace transforms is developed. The theorem regarding the independence of the final image (final original) on the sequence of realizing the transforms is proved. The diffusion equation with delay is analytically exactly resolved. An algorithm of the solution is given for cases \xi>>\gamma and arbitrary values of parameter \gamma. It has been shown what changes in solution take place for problems of diffusion with a moving boundary. The solution may be used for most problems with a delay argument.
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