On a System Without Critical Points Arising in Heat Conductivity Theory

Samuilik, Inna; Sadyrbaev, Felix

doi:10.37394/232012.2022.17.17

1790-5044

2022

DOI: 10.37394/232012.2022.17.17

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On a System Without Critical Points Arising in Heat Conductivity Theory

Inna Samuilik¹,

Felix Sadyrbaev

Abstract: A two-point boundary value problem for the second order nonlinear ordinary differential equation, arising in the heat conductivity theory, is considered. Multiplicity and existence results are established for this problem, where the equation contains two parameters.

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Cited by 2 publications

References 16 publications

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On differential equations with exponential nonlinearities

Gritsans,

Sadyrbaev

2025

Applied Numerical Mathematics

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On differential equations with exponential nonlinearities

Gritsans,

Sadyrbaev

2025

Applied Numerical Mathematics

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On the Stability of a Convective Flow with Nonlinear Heat Sources

Gritsans,

Kolyshkin,

Sadyrbaev

et al. 2023

Mathematics

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The linear stability of a convective flow in a vertical fluid layer caused by nonlinear heat sources in the presence of cross-flow through the walls of the channel is investigated in this paper. This study is relevant to the analysis of factors that affect the effectiveness of biomass thermal conversion. The nonlinear problem for the base flow temperature is investigated in detail using the Krasnosel’skiĭ–Guo cone expansion/contraction theorem. It is shown that a different number of solutions can exist depending on the values of the parameters. Estimates for the norm of the solutions are obtained. The linear stability problem is solved numerically by a collocation method based on Chebyshev polynomials. It is shown that the increase in the cross-flow intensity stabilizes the flow, but there is also a small region of the radial Reynolds numbers where the flow is destabilized.

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On a System Without Critical Points Arising in Heat Conductivity Theory

Abstract: A two-point boundary value problem for the second order nonlinear ordinary differential equation, arising in the heat conductivity theory, is considered. Multiplicity and existence results are established for this problem, where the equation contains two parameters.

Cited by 2 publications

References 16 publications

On differential equations with exponential nonlinearities

On differential equations with exponential nonlinearities

On the Stability of a Convective Flow with Nonlinear Heat Sources

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