Properties of Solutions in a Fourth‑Order Equation of Squeezing Flows

摘要

We investigate properties of solutions for a squeezing flow problem governed by a fourth-order nonlinear ODE. The findings obtained reveal significant mathematical features with crucial physical implications. Those findings are obtained via the use of appropriate mathematical equations and approximations, as well as very careful mathematical analysis and derivations, which lead to mathematical formulas for relevant parameters, and results that enable us achieve a new understanding for the physical problem. The derived formulas for the parameters are compared with computations obtained using MATLAB built-in integrators to illustrate the accuracy of those derived formulas. In addition to doing the computations and generating the tabulated results, the MATLAB software is used to generate the figures and illustrations which highlight the main results and conclusions. Existence of solutions is discussed, and some special case solutions are obtained. Properties of parameters and their interdependence are determined, where relevant relations are derived.