To the properties of solutions of the Cauchy problem for degenerate nonlinear cross systems with absorption

The conditions of finite speed propagation disturbance and a space localization, free boundary of the solutions of the Cauchy problem for the cross system with variable density is established. An approximately self-similar system for obtaining self-similar approximate solutions is constructed, the property of the finite velocity of the perturbation propagation is determined. Asymptotes of self-similar solutions will also be constructed.

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