On the solutions of a boundary value problem arising in free convection with prescribed heat flux

Abstract

For given a ∈ R, c < 0, we are concerned with the solution f b of the differential equation f + ff + g(f ) = 0 satisfying the initial con-This allows to answer questions about existence, uniqueness and boundedness of solutions to a boundary value problem arising in fluid mechanics, and especially in boundary layer theory.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

“…where a < t 1 < t 2 < t 3 < b and y 1 , y 2 , y 3 ∈ R. Third-order ordinary differential equations arise as models for certain natural phenomena such as boundary-layer flow in fluid mechanics involving convection in a porous medium, or a flow along a standing wall or stretched sheet (see [1,4,6,16,[47][48][49]51,52]). Other theoretical works have dealt with third-order equations devoted to, for example, upper and lower solutions, periodic solutions, limit-point and limit-circle criteria and singular boundary-value problems (see [2,3,5,32,36,41,45,50]).…”

Existence of Strong Solutions for Nonlinear Systems of PDEs Arising in Convective Flow

“…In the framework of boundary layer approximations, by introducing similarity variables, we can transform the system of partial differential equations into a system of ordinary differential equations of the third order with appropriate boundary values (see [1], p.3). ese two-point boundary value problems can be studied by using a shooting method (see for example [2,3]). For the auxiliary dynamical system, we refer the reader to [4].…”

Similarity solutions of mixed convection boundary-layer flows in a porous medium

“…For g(x) = βx 2 , this corresponds to free convection problems, see for example [16] for the derivation of the model, and [2], [4], [7], [8], [11], [14], [15], [18], [23], [25] for different approaches of the mathematical analysis.…”

“…The boundary value problems associated to the general equation (2), with the condition that f ′ tends to λ at infinity have been studied in [13] and in [9]. Let us notice that, if g(λ) = 0, then these boundary value problems do not have any solutions, and thus we must assume that g(λ) = 0 to have solutions.…”