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A note on the extended Blasius equation. (English) Zbl 1126.34301

The authors discuss the possibility of applying the classical Blasius flat-plate equation to solve the third-order differential equation
\[ af'''(\eta)+ f(\eta) f''(\eta)= 0 \]
with the boundary conditions
\[ f(0)= f'(0)= 0\quad\text{and}\quad f'(\infty)= 1. \]
It is shown that the solution of this boundary value problem for an arbitrary value of \(a\) can be obtained from the classical Blasius equation with \(a=1\) after a variable transformation.

MSC:

34A05 Explicit solutions, first integrals of ordinary differential equations
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
34B15 Nonlinear boundary value problems for ordinary differential equations
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References:

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