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.


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