Two numerical methods for finding multiple solutions of a superlinear Dirichlet problem

Afrouzi, G. A.; Naghizadeh, Z.; Mahdavi, S.

doi:10.1016/j.amc.2006.10.072

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Proposition 131

Remark 141

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2009

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“…We conclude that lim t→∞ f − m α f ′ = L α . Finally, a simple integration leads to estimate (20). To finish, we pay attention to the case m = −α.…”

Section: Proposition 13mentioning

confidence: 99%

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Similarity Flow Solutions of a Non-Newtonian Power-law Fluid

Guedda,

Hammouch

2009

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In this paper we present a mathematical analysis for a steady-state laminar boundary layer flow, governed by the Ostwald-de Wael power-law model of an incompressible non-Newtonian fluid past a semi-infinite power-law stretched flat plate with uniform free stream velocity. A generalization of the usual Blasius similarity transformation is used to find similarity solutions [1]. Under appropriate assumptions, partial differential equations are transformed into an autonomous third-order nonlinear degenerate ordinary differential equation with boundary conditions. Using a shooting method, we establish the existence of an infinite number of global unbounded solutions. The asymptotic behavior is also discussed. Some properties of those solutions depend on the viscosity power-law index.

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“…We conclude that lim t→∞ f − m α f ′ = L α . Finally, a simple integration leads to estimate (20). To finish, we pay attention to the case m = −α.…”

Section: Proposition 13mentioning

confidence: 99%

“…According to Proposition 13, f f ′ goes to infinity with t and then the left hand side of the above is integrable, consequently f m f ′−α has a positive finite limit at infinity. The desired asymptotic behavior (20) follows by a simple integration. Now we deal with the case m + α < 0.…”

Section: Remark 14mentioning

confidence: 99%

Similarity Flow Solutions of a Non-Newtonian Power-law Fluid

Guedda,

Hammouch

2009

Preprint

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Two numerical methods for finding multiple solutions of a superlinear Dirichlet problem

Cited by 1 publication

References 3 publications

Similarity Flow Solutions of a Non-Newtonian Power-law Fluid

Similarity Flow Solutions of a Non-Newtonian Power-law Fluid

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