Abstract
The aim of this article was to provide analytical and numerical approaches to a one-dimensional Eyring-Powell flow. First of all, the regularity, existence, and uniqueness of the solutions were explored making use of a variational weak formulation. Then, the Eyring-Powell equation was transformed into the travelling wave domain, where analytical solutions were obtained supported by the geometric perturbation theory. Such analytical solutions were validated with a numerical exercise. The main finding reported is the existence of a particular travelling wave speed a=1.212 for which the analytical solution is close to the actual numerical solution with an accumulative error of < 10(-3).