Yoshitaka Watanabe:
A Numerical Verification Method for Two-Coupled Elliptic Partial Differential Equations,
Japan Journal of Industrial and Applied Mathematics, Vol. 26, No. 2-3 (October 2009) pp. 233-247.

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.

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