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Dual solutions of boundary layer flow over an upstream moving plate. (English) Zbl 1131.35066
Summary: The homotopy analysis method is applied to study the boundary layer flow over a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream. The dual solutions in series expressions are obtained with the proposed technique, which agree well with numerical results. Note that, by introducing a new auxiliary function $$\beta (z)$$, the bifurcation of the solutions is obtained. This indicates that the homotopy analysis method is an open system, in the framework of this technique, we have great freedom to choose the auxiliary parameters or functions. As a result, complicated nonlinear problems may be resolved in a simple way. The present work shows that the homotopy analysis method is an effective tool for solving nonlinear problems with multiple solutions.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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