Mathematics – Dynamical Systems
Scientific paper
2007-07-11
Mathematics
Dynamical Systems
Scientific paper
For given $a\in\R$, c<0, we are concerned with the solution $f^{}_b$ of the differential equation $f^{\prime\prime\prime}+ff^{\prime\prime}+\g(f^{\prime})=0$, satisfying the initial conditions $f(0)=a$, $f'(0)=b$, $f''(0)=c< 0$, where g is some nonnegative subquadratic locally Lipschitz function. It is proven that there exists $b_*>0$ such that $f^{}_b$ exists on $[0,+\infty)$ and is such that $f'_b(t)\to 0$ as $t\to+\infty$, if and only if $b\geq b_*$. This allows to answer questions about existence, uniqueness and boundedness of solutions to a boundary value problem arising in fluid mechanics, and especially in boundary layer theory.
Aïboudi Mohamed
Brighi Bernard
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