Article

Global existence and nonexistence for a multidimensional system of parabolic equations with nonlinear boundary conditions

Zafar Rakhmonov)National university of Uzbekistan, Tashkent, UzbekistanRoman Parovik)Kamchatka State University named after Vitus Bering, RussiaA.A. Alimov)National university of Uzbekistan, Tashkent, Uzbekistan

AIP conference proceedingsjournal2021en

ABI

Abstract

In this paper, we study the conditions of global solvability and unsolvability in time of solutions to the nonlinear diffusion problem based on self-similar analysis. We constructed various self-similar solutions of the nonlinear diffusion problem in the slow diffusion case. We established critical exponents of the Fujita type and critical exponents for the global existence of the solution. Using the asymptotic formulas as the initial approximation for the iterative process, numerical calculations are performed.

Topics

Advanced Mathematical Modeling in Engineering Differential Equations and Numerical Methods Differential Equations and Boundary Problems

Identifiers

DOI: 10.1063/5.0057139

Citations and references

Cited by 5 20 references

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