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- W2899493810 abstract "In this paper, we are concerned with the solution of the third-order nonlinear differential equation <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mo>″</mml:mo><mml:mi mathvariant=normal>′</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>f</mml:mi><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mo>″</mml:mo></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>β</mml:mi><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=normal>′</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=normal>′</mml:mi></mml:mrow></mml:msup><mml:mo>-</mml:mo><mml:mn mathvariant=normal>1</mml:mn><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant=normal>0</mml:mn></mml:math>, satisfying the boundary conditions <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mn mathvariant=normal>0</mml:mn><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant=double-struck>R</mml:mi></mml:math>, <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=normal>′</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:mn mathvariant=normal>0</mml:mn><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mi>b</mml:mi><mml:mo><</mml:mo><mml:mn mathvariant=normal>0</mml:mn></mml:math>, and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=normal>′</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>→</mml:mo><mml:mi>λ</mml:mi></mml:math>, as <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>t</mml:mi><mml:mo>→</mml:mo><mml:mo>+</mml:mo><mml:mi mathvariant=normal>∞</mml:mi></mml:math>, where <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi>λ</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=false>{</mml:mo><mml:mn mathvariant=normal>0,1</mml:mn><mml:mo stretchy=false>}</mml:mo></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mn mathvariant=normal>0</mml:mn><mml:mo><</mml:mo><mml:mi>β</mml:mi><mml:mo><</mml:mo><mml:mn mathvariant=normal>1</mml:mn><mml:mo>.</mml:mo></mml:math> The problem arises in the study of the opposing mixed convection approximation in a porous medium. We prove the existence, nonexistence, and the sign of convex and convex-concave solutions of the problem above according to the mixed convection parameter <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mi>b</mml:mi><mml:mo><</mml:mo><mml:mn mathvariant=normal>0</mml:mn></mml:math> and the temperature parameter <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mn mathvariant=normal>0</mml:mn><mml:mo><</mml:mo><mml:mi>β</mml:mi><mml:mo><</mml:mo><mml:mn mathvariant=normal>1</mml:mn></mml:math>." @default.
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- W2899493810 date "2018-11-01" @default.
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- W2899493810 title "On the Convex and Convex-Concave Solutions of Opposing Mixed Convection Boundary Layer Flow in a Porous Medium" @default.
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- W2899493810 doi "https://doi.org/10.1155/2018/4340204" @default.
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