Density profile equation with p-Laplacian: Analysis and numerical simulation

Analytical properties of a nonlinear singular second order boundary value problem in ordinary differential equations posed on an unbounded domain for the density profile of the formation of microscopic bubbles in a nonhomogeneous fluid are discussed. Especially, sufficient conditions for the existence and uniqueness of solutions are derived. Two approximation methods are presented for the numerical solution of the problem, one of them utilizes the open domain Matlab code bvpsuite. The results of numerical simulations are presented and discussed.