A BVP nonexistence proof using Green's Theorem. (June 2017)

• Record Type: Journal Article
• Authors: Previte, Joseph P.; Paullet, Joseph E.
• Is Part Of: Applied mathematics letters. Volume 68(2017:Jun.)
• Page Start: 171
• Page End: 174
• Publication Date: 2017-06
• Subjects: Boundary value problem -- Nonexistence -- Green's Theorem; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2017.01.009
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: Several recent papers investigate the boundary value problem ϕ ′ ′ ( t ) + λ ϕ ′ ( t ) + ϕ ( t ) 2 = 0, t ≥ 0 subject to ϕ ( 0 ) = 1, ϕ ( ∞ ) = 0, which arises in certain situations of boundary layer flow. Previous work on the problem established the existence of a λ min ∈ [ 1, 2 ∕ 3 ] such that solutions exist for λ ≥ λ min . It has been conjectured that for λ < λ min no solution exists. We improve existing results by proving that for λ < λ 1 ≈ . 96105 no solution to the boundary value problem exists. The proof employs a novel application of Green's Theorem and is applicable to other boundary value problems.