Bifurcation analysis of nonlinear reaction-diffusion problems using wavelet-based reduction techniques

@article{Krishnan2004BifurcationAO,
  title={Bifurcation analysis of nonlinear reaction-diffusion problems using wavelet-based reduction techniques},
  author={J. Krishnan and Olof Runborg and Ioannis G. Kevrekidis},
  journal={Computers & Chemical Engineering},
  year={2004},
  volume={28},
  pages={557-574}
}
Using a computational method for numerical homogenization, we perform the coarse-scale bifurcation analysis of nonlinear reaction–diffusion problems in both uniform and spatially varying media. The method is based on wavelet decomposition and projection of the differential equation on coarse scale wavelet spaces. The approach is capable of capturing turning points and pitchfork bifurcations of sharp, front-like solutions at the coarse level. © 2003 Elsevier Ltd. All rights reserved. 

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