Boundary value problem with integral condition for a Blasius type equation

• Main Author: Sergey Smirnov
• Format: Article
• Language: English
• Published: Vilnius University Press 2016-01-01
• Series: Nonlinear Analysis
• Subjects: boundary layer; Blasius equation; integral boundary conditions; existence and uniqueness of solutions
• Online Access: http://www.journals.vu.lt/nonlinear-analysis/article/view/13501

The steady motion in the boundary layer along a thin flat plate, which is immersed at zero incidence in a uniform stream with constant velocity, can be described in terms of the solution of the differential equation x'''= -xx'', which satisfies the boundary conditions x(0) = x'(0) = 0, x'(∞) = 1. The author investigates the generalized boundary value problem consisting of the nonlinear third-order differential equation x''' = -trx|x|q-1x'' subject to the integral boundary conditions x(0) = x'(0) = 0, x'(∞) = λ∫0ξx(s) ds, where 0 < ξ < +∞ is a fixed number and λ > 0 is a parameter. Results on the existence and uniqueness of solutions to boundary value problem are established. An illustrative example is provided.