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By means of the method of hybrid integral transform of Euler-Fourier-Bessel type with spectral parameter the integral representation of exact analytical solution of mixed problem for the system of equations of parabolic type in the three-part segment Œ0;R is obtained under the assumption that the limits are soft. Modeling of evolutionary processes is performed by the method of hybrid differential Euler-Fourier-Bessel operators. 2010 Mathematics Subject Classification: 34D20

The integral representation of the solution of some mixed problem for evolutionary equations