Nonexistence for the "missing" similarity boundary-layer flow

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which arises in certain situations of boundary layer flow. Previous work on the problem established the existence of a λmin ∈ [1; 2/√3] such that solutions exist for λ ≥ λmin. It has been conjectured that for λ < λmin no solution exists. We partially resolve this conjecture by proving that for λ ≤√2/3 ≈:8165 no solution to the boundary value problem exists.

This note considers the boundary value problem.

ϕʺ(η) + λϕʹ(η) + ϕ(η)2 = 0, η ≥ 0, λ > 0,.

subject to.

ϕ(0) = 1 and ϕ(∞) = 0,.

Original languageEnglish (US)
Pages (from-to)123-126
Number of pages4
JournalApplied Mathematics E - Notes
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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