A numerical verification method for two-coupled elliptic partial differential equations

@article{Watanabe2009ANV,
  title={A numerical verification method for two-coupled elliptic partial differential equations},
  author={Yoshitaka Watanabe},
  journal={Japan Journal of Industrial and Applied Mathematics},
  year={2009},
  volume={26},
  pages={233-247}
}
  • Y. Watanabe
  • Published 2009
  • Mathematics
  • Japan Journal of Industrial and Applied Mathematics
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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