• Corpus ID: 208267949

Spectral analysis for singularity formation of the two dimensional Keller-Segel system.

  title={Spectral analysis for singularity formation of the two dimensional Keller-Segel system.},
  author={Charles Collot and Tej-eddine Ghoul and Nader Masmoudi and Van Tien Nguyen},
  journal={arXiv: Analysis of PDEs},
We analyse an operator arising in the description of singular solutions to the two-dimensional Keller-Segel problem. It corresponds to the linearised operator in parabolic self-similar variables, close to a concentrated stationary state. This is a two-scale problem, with a vanishing thin transition zone near the origin. Via rigorous matched asymptotic expansions, we describe the eigenvalues and eigenfunctions precisely. We also show a stability result with respect to suitable perturbations, as… 
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