## On the analytic solutions of the nonhomogeneous Blasius problem.(English)Zbl 1071.65108

Summary: A totally analytic solution of the nonhomogeneous Blasius problem is obtained using the homotopy analysis method. This solution converges for $$0\leqslant \eta < \infty$$. Existence and nonuniqueness of solution is also discussed. An implicit relation between the velocity at the wall $$\lambda$$ and the shear stress $$\alpha=f''(0)$$ is obtained. The results presented here indicate that two solutions exist in the range $$0 < \lambda < \lambda_c$$, for some critical value $$\lambda_c$$ one solution exists for $$\lambda=\lambda_c$$, and no solution exists for $$\lambda > \lambda_c$$. An analytical value of the critical value of $$\lambda_c$$ is also obtained for the first time.

### MSC:

 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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### References:

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