A numerical verification method of steady state solutions for a system of reaction-diffusion equations is described. Using a decoupling technique, the system is reduced to a single nonlinear equation and a computer-assisted method for second-order elliptic boundary value problems based on the infinite dimensional fixed-point theorem can be applied. Some numerical examples confirm the effectiveness of the method.
"A Numerical Verification Method for Two-Coupled Elliptic Partial Differential Equations." Japan J. Indust. Appl. Math. 26 (2-3) 233 - 247, October 2009.