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The paper presents a mathematical model the collision process of rotating molecular clouds. The collision of molecular clouds can lead either to their destruction or to the formation of dense clumps. These dense clumps can lead to the formation of gravitationally bound areas. Such gravitationally bound regions are one of the main processes of star formation. In this work, the processes of central and off-center collisions of cold isothermal and non-isothermal rotating molecular clouds are studied numerically. Numerical modeling makes it possible to study in detail the formation and destruction of filaments, the formation of dense clumps, which, under certain conditions, become the embryos of new stars. The process of destruction and fragmentation of the MC gas was studied using the results of the evolution of the density of a molecular cloud with different density distributions along the radius, different collision velocities and rotation rates. Calculations have shown that at some points in time, very dense formations of gas fractions are formed, the density of which is many orders of magnitude higher than the initial density. Apparently, it is caused by turbulent supersonic shock compression and is associated with the formation of transitional filamentous rudimentary structures.