Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak-Keller-Segel Model

@article{Blanchet2008ConvergenceOT,
  title={Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak-Keller-Segel Model},
  author={Adrien Blanchet and Vincent Calvez and Jos{\'e} A. Carrillo},
  journal={SIAM J. Numerical Analysis},
  year={2008},
  volume={46},
  pages={691-721}
}
Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel… CONTINUE READING

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