Article

On the behavior of solutions for a system of multidimensional diffusion equations with nonlinear boundary conditions

Zafar RakhmonovNational University of Uzbekistan named after Mirzo Ulugbek, University Street 4, Tashkent, 100174, UzbekistanA.A. AlimovNational University of Uzbekistan named after Mirzo Ulugbek, University Street 4, Tashkent, 100174, UzbekistanJasur UrunbaevDigital Technologies and Artificial Intelligence Research Institute Boz-2, 17A, Tashkent, 100125, Uzbekistan

AIP conference proceedingsjournal2024en

ABI

Abstract

In this paper, we study the conditions of global solvability and unsolvability in time of solutions to the system of multidimensional diffusion equations with nonlinear boundary conditions. We constructed various self-similar solutions of the system of multidimensional diffusion equations in the slow diffusion case. We established critical exponents of the Fujita type and critical exponents for the global existence of the solution.

Topics

Nonlinear Differential Equations Analysis Differential Equations and Numerical Methods Stability and Controllability of Differential Equations

Identifiers

DOI: 10.1063/5.0194896

Citations and references

Cited by 1 15 references

Metrics — AkademScholar · Coming soon