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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 0η<. Existence and nonuniqueness of solution is also discussed. An implicit relation between the velocity at the wall λ and the shear stress α=f '' (0) is obtained. The results presented here indicate that two solutions exist in the range 0<λ<λ c , for some critical value λ c one solution exists for λ=λ c , and no solution exists for λ>λ c . An analytical value of the critical value of λ c is also obtained for the first time.
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE