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In this paper, we study the condition of global existence and non-existence of a solution of a nonlinear parabolic system with a nonlinear boundary condition and with a variable density. Estimate of solutions, asymptotic behavior of self-similar solutions depending on the value of numerical parameters of the system of the process under study is established for the case of slow and fast diffusion and for the critical case. The influence of variable density on the estimation of solutions, in critical cases, behavior of solutions is considered.
Арипов et al. (Mon,) studied this question.
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