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The asymptotic solution of a family of boundary value problems involving exponentially small terms. (English) Zbl 0815.76081

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.

MSC:

76S05 Flows in porous media; filtration; seepage
78A25 Electromagnetic theory (general)
34E15 Singular perturbations for ordinary differential equations
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