Grundy, R. E.; Allen, H. R. The asymptotic solution of a family of boundary value problems involving exponentially small terms. (English) Zbl 0815.76081 IMA J. Appl. Math. 53, No. 2, 151-168 (1994). We consider the family of boundary value problems \(\varepsilon f^{\text{(iv)}}- ff''' + f'f'' = 0\), \(f(0) = f''(0) = 0\), \(f(1) = 1\), \(f''(1) = -\alpha\), in the limit \(| \varepsilon| \to 0\). Using a combination of asymptotic and numerical analyses, the paper gives a comprehensive treatment of the problem, paying particular attention to the question of duality of solutions. Cited in 1 Document MSC: 76S05 Flows in porous media; filtration; seepage 78A25 Electromagnetic theory (general) 34E15 Singular perturbations for ordinary differential equations Keywords:scaling method; one-parameter family of problems of initial value type; magnetic field annihilation; duality of solutions PDFBibTeX XMLCite \textit{R. E. Grundy} and \textit{H. R. Allen}, IMA J. Appl. Math. 53, No. 2, 151--168 (1994; Zbl 0815.76081) Full Text: DOI