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| The talk is concerned with the global in time solutions of the Cauchy problem for waves propagating in the curved spacetime, which can be, in particular, modeled by cosmological models. We examine the global in time solutions of some class of semililear hyperbolic equations in the de~Sitter spacetime. The crucial tool for the obtaining those results is a new approach, which is based on the integral transform with the kernel containing the hypergeometric function. That integral transform allows to write solutions of the initial-value problem for one partial differential equation via solution of another one. |
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