on Intelligent Manufacturing and Automation , 2013 Behavior of Integral Curves of the Quasilinear Second Order Differential Equations
This paper deals with certain classes of Cauchy’s solutions of quasilinear second order differential equations in general form, Van der Pol's differential equation, which is used in the theory of electric circuits, and Lagerstorm's differential equations, which is used in asymptotic treatment of viscous flow past a solid at low Reynolds number. Behaviour of integral curves in the neighbourhoods of an arbitrary or integral curve is considered. Obtained results establish sufficient conditions for the existence and asymptotic behaviour of the observed equations. The obtained results contain the answer to the question on approximation of solutions whose existence is established. The errors of the approximation are defined by functions that can be sufficiently small. The qualitative analysis theory and topological retraction methods were used. © 2014 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of DAAAM International Vienna.