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Using the mathematical apparatus of the multifactor regression analysis, the concept of faults between civilizations is verified, formalized and refined. The ethnocultural civilizational distribution of the countries is specified on the basis of the fuzzy cluster method. The mathematical model of fault lines between civilizations is elaborated, which affords the opportunity to estimate and analyze the quantitative values of these faults. Formally, the developed model offers the way to determine evolutionary regularities, systematize and econometrically verify the defining characteristics of actual civilizational clashes. The results of an analysis and comparison of modeling data of intercivilizational faults in 2008 and 2018 revealed the tendencies of individual civilizations to unite and clash, and the effect of these faults on the global conflict as well. The dependence of global threats on the proliferation of weapons and their individual components is assessed. The conflict effect on the socio-economic indicators of clashing civilizations is determined. The correspondence of the modeling outcomes to the real state of intercivilizational faults is verified by comparison with actual historical data. The results of the study encourage to form a comprehensive vision of the nature of modern clashes, whose emergence is caused by the faults between civilizations, and to determine their formal characteristics and regularities of their course.

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We obtain conditions to find the distributed optimal control for parabolic-hyperbolic equations with nonlocal boundary conditions and general quadratic criterion in the special norm. The unique solvability of systems for finding the optimal solution is established, systems' kernels are estimated, and the convergence of solutions of the problem is proved.