On the asymptotic behaviour of solutions of some nonlinear elliptic and parabolic equations Original Research Article

In this paper, we investigate the spatial asymptotic behaviour of some nonlinear elliptic and parabolic equations related with the process of diffusion–convection. We obtain results of the kind of the Phragmén–Lindelof alternative. The main idea of the paper is to obtain a nonlinear ordinary differential inequality which is satisfied by a certain measure of the solutions. This ordinary inequality was studied by Horgan and Payne in a recent paper. We obtain our results with the help of estimates known for this inequality. When the solutions tend to zero, we also obtain an estimate for the amplitude term.