EXACT AND APPROXIMATE SOLUTIONS OF A DEGENERATE REACTION-DIFFUSION SYSTEM

We consider the problem of constructing exact solutions to a system of two coupled nonlinear parabolic reaction-diffusion equations. We study solutions in the form of diffusion waves propagating over zero background with a finite speed. The theorem on the construction of exact solutions by reducing to the Cauchy problem for a system of ordinary differential equations (ODEs) is proved. A time-step numerical technique for solving the reaction-diffusion system using radial basis function expansion is proposed. The same technique is used to solve the systems of ordinary differential equations defining exact solutions to the reaction-diffusion system. Numerical analysis and estimation of the accuracy of solutions to the system of ODEs are carried out. These solutions are used to verify the obtained time-step solutions of the original system..