Premium
On the Asymptotic Behaviour of Solutions of a Differential Equation in Boundary Layer Theory
Author(s) -
Hartman Philip
Publication year - 1964
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19640440307
Subject(s) - mathematics , mathematical analysis , boundary value problem , image (mathematics) , differential equation , computer science , artificial intelligence
The asymptotic behavior, as t → ∞, of solutions of the singular boundary value problem u′′ + u u′ + λ (1 − u′ 2 ) = 0, u′ (0) = α, u′ (0) = β and u′ (∞) = 1, subject to 0 < u′(t) < 1 for 0 < t < ∞, is discussed. It is shown that if λ ≥ 0 and if the solution u exists, then (1). If λ < 0 and if a solution exists, then there is a unique one satisfying (1) while the other (if any) satisfy (2).