Abstract:

The paper considers solutions with zero fronts to a system of two degenerate nonlinear (quasilinear) parabolic equations. Such systems are used in mathematical biology to describe population dynamics, specifically in the "predator-prey" models. The study focuses on a special case, where the zero fronts of two unknown functions, specified by the boundary conditions, move in opposite directions. We prove a new theorem of the existence and uniqueness of an analytical solution to the problem under consideration and derive new exact solutions by reducing the original system to a system of ordinary differential equations in a particular case. A stepwise numerical algorithm based on the collocation method and radial basis functions is proposed. Finally, we conduct a qualitative and quantitative analysis of analytical and numerical solutions, utilizing the exact solutions to verify the numerical algorithm.