2015/06/09 by Mohammed Aiboudi, Aiboudi, Mohammed, Ikram Bensari-Khelil +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS
paper · pdf · doi:10.48550/arxiv.1506.02835
arxiv created 2015/06/09 · arxiv updated 2015/06/10
The similarity differential equation f'''+ff''+βf'(f'-1)=0 with β\textgreater0 is considered. This differential equation appears in the study of mixed convection boundary-layer flows over a vertical surface embedded in a porous medium. In order to prove the existence of solutions satisfying the boundary conditions f(0)=a≥0, f'(0)=b≥0 and f'(+∞)=0 or 1, we use shooting and consider the initial value problem consisting of the differential equation and the initial conditions f(0)=a, f'(0)=b and f''(0)=c. For 0\textlessβ≤1, we prove that there exists a unique solution such that f'(+∞)=0, and infinitely many solutions such that f'(+∞)=1. For β\textgreater1, we give only partial results and show some differences with the previous case.