Attractors in confined source problems for coupled nonlinear diffusion
In processes driven by nonlinear diffusion a signal from a concentrated source remains confined in a finite region in space during the dynamics. Such kind of solutions appears in numerous applied problems such as gas filtration and turbulent flows. Due to their confined shape the solutions are convenient to seek in the form of power series in spatial coordinate. The original set of PDEs is converted to a dynamical system with respect to time-dependent series coefficients to analyze. We use this approach in problems involving coupled agents. To test the method we consider a single equation with linear and then quadratic diffusivity to recover the known results. Then we apply the approach to modeling of expanding free turbulent jet. Some example trajectories for the respective dynamical system are presented. The structure of the system hints an existence of an attracting centre manifold. The attractor is explicitly found for a reduced version of the system.
