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..