Analysis and numerics of traveling waves for asymmetric fractional reaction-diffusion equations

@article{Achleitner2014AnalysisAN,
  title={Analysis and numerics of traveling waves for asymmetric fractional reaction-diffusion equations},
  author={F. Achleitner and C. K{\"u}hn},
  journal={arXiv: Numerical Analysis},
  year={2014}
}
  • F. Achleitner, C. Kühn
  • Published 2014
  • Mathematics, Physics
  • arXiv: Numerical Analysis
  • We consider a scalar reaction-diffusion equation in one spatial dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. We present our analytical results on the existence, uniqueness (up to translations) and stability of a traveling wave solution connecting two stable homogeneous steady states. Moreover, we review numerical methods for the case of reaction-diffusion equations with fractional Laplacian and discuss possible extensions to our… CONTINUE READING

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